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We characterise the entire set of symmetric stationary Markov-perfect Nash equilibria (MPE) in a differential game of public good investment, using the canonical problem of climate change as an example. We provide a sufficient and necessary condition for MPE and show how the entire set of MPE is constructed. The equilibrium in continuous strategies, unique in our context, is Pareto-dominated by any other equilibrium. If a Pareto- undominated steady state exists, it is sustained by trigger-like strategies, with deviations above and below the steady state leading to different re- sponses. We extend the theory of differential games to deal with payoffs under discontinuous strategies. Our methods work under general functional forms.

Although there exist learning processes for which the empirical distribution of play comes close to Nash equilibrium it is an open question whether the players themselves can learn to play equilibrium strategies without assuming that they have prior knowledge of their opponents' strategies and/or payoffs We exhibit a large class of statistical hypotheses testing procedures that solve this problem Consider a finite stage game G that is repeated infinitely often At each time the players have hypotheses about their opponents' repeated game strategies They frequently test their hypotheses against the opponents' recent actions When a hypotheses fails test a new one is adopted Play is almost rational in the sense that at each point of time the players' strategies are є -best replies to their beliefs We show that at least 1 - є of the time t these hypotheses testing strategies constitute an є-equilibrium of the repeated game from t on; in fact the strategies are close to being subgame perfect for long stretches of time Further all players for whom prediction matters ie whose best responses depend on the opponents' behavior learn to predict within є.

In this paper the problem of optimal derivative design, profit maximization and risk minimization under adverse selection when multiple agencies compete for the business of a continuum of heterogenous agents is studied. The presence of ties in the agents' best-response correspondences yields discontinuous payoff functions for the agencies. These discontinuities are dealt with via efficient tie--breaking rules. In a first step, the model presented by Carlier, Ekeland & Touzi (2007) of optimal derivative design by profit-maximizing agencies is extended to a multiple--firm setting, and results of Page & Monteiro (2003, 2007, 2008) are used to prove the existence of (mixed-strategies) Nash equilibria. On a second step we consider the more complex case of risk minimizing firms. Here the concept of socially efficient allocations is introduced, and existence of the latter is proved. It is also shown that in the particular case of the entropic risk measure, there exists an efficient "fix--mix" tie-breaking rule, in which case firms share the whole market over given proportions., 34 pages and 6 figures

Quasilinear preferences on a public good and a numeraire good are limits of preferences where both goods are normal. The set of equilibria of the voluntary contribution (or private provision) game is easily characterized under quasilinearity by: top valuators aggregately contribute their common stand-alone contribution, whereas non-top valuators contribute nothing. Because, as long as preferences are randomly selected, there will typically be a single top valuator, it follows that, typically, the equilibrium is unique, with all players but one contributing nothing, hence “free riding” in the sense of the ordinary English usage of the expression. The upper-hemicontinuity of the Nash equilibrium correspondence implies that this is also the case when both goods are strictly normal, but the wealth effects on the public good are small.

Howard (J Econ Theory 56: 142-159, 1992) argues that the Nash bargaining solution is not Nash implementable, as it does not satisfy Maskin monotonicity. His arguments can be extended to other bargaining solutions as well. However, by defining a social choice correspondence that is based on the solution rather than on its realizations, one can overcome this shortcoming. We even show that such correspondences satisfy a stronger version of monotonicity that is even sufficient for Nash implementability.

We study a structural model of R&D alliance networks in which firms jointly form R&D collaborations to lower their production costs while competing on the product market. We derive the Nash equilibrium of this game, provide a welfare analysis and determine the optimal R&D subsidy program that maximizes total welfare. We also identify the key firms, i.e. the firms whose exit would reduce welfare the most. We then structurally estimate our model using a panel dataset of R&D collaborations and annual company reports. We use our estimates to identify the key firms and analyze the impact of R&D subsidy programs. Moreover, we analyze temporal changes in the rankings of key firms and how these changes affect the optimal R&D policy.

Biconcavity is a simple condition on inverse demand that corresponds to the ordinary concept of concavity after simultaneous parameterized transformations of price and quantity. The notion is employed here in the framework of the homogeneous-good Cournot model with potentially heterogeneous firms. The analysis leads to unified conditions, respectively, for the existence of a pure-strategy equilibrium via nonincreasing best-response selections, for existence via quasiconcavity, and for the uniqueness of the equilibrium. The usefulness of the generalizations is illustrated in cases where inverse demand is either “nearly linear” or isoelastic. It is also shown that commonly made assumptions regarding large outputs are often redundant.

We call a correspondence, defined on the set of mixed strategy profiles, a generalized best reply correspondence if it (i) has a product structure, (ii) is upper hemicontinuous, (iii) always includes a best reply to any mixed strategy profile, and (iv) is convex-and closed-valued. For each generalized best reply correspondence, we define a generalized best reply dynamics as a differential inclusion based on it. We call a face of the set of mixed strategy profiles a minimally asymptotically stable face (MASF) if it is asymptotically stable under some such dynamics and no subface of it is asymptotically stable under any such dynamics. The set of such correspondences (and dynamics) is endowed with the partial order of pointwise set inclusion and, under a mild condition on the normal form of the game at hand, forms a complete lattice with meets based on pointwise intersections. The refined best reply correspondence is then defined as the smallest element of the set of all generalized best reply correspondences. We find that every persistent retract (Kalai and Samet 1984) contains a MASF. Furthermore, persistent retracts are minimal CURB (closed under rational behavior) sets (Basu and Weibull 1991) based on the refined best reply correspondence. Conversely, every MASF must be a prep set (Voorneveld 2004), based again, however, on the refined best reply correspondence.

In a number of large, important families of finite games, not only do pure-strategy Nash equilibria always exist but they are also reachable from any initial strategy profile by some sequence of myopic single-player moves to a better or best-response strategy. This weak acyclicity property is shared, for example, by all perfect-information extensive-form games, which are generally not acyclic since even sequences of best-improvement steps may cycle. Weak acyclicity is equivalent to the existence of weak potential, which unlike a potential increases along some rather than every sequence as above, as well as to the existence of an acyclic scheduler, which guarantees convergence to equilibrium by disallowing certain (improvement) moves. A number of sufficient conditions for acyclicity and weak acyclicity are known.

We present an economic experiment on network formation, in which subjects can decide to form links to one another. Direct links are costly but being connected is valuable. The gametheoretic basis for our experiment is the model of Bala and Goyal (2000). They distinguish between two scenarios regarding the flow of benefits through a network, the so-called 1-way and 2-way flow model. Our main results show that the prediction based on Nash and strict Nash equilibrium works well in the 1-way flow model but fails largely in the 2-way flow model. We observe a strong learning dynamic in the 1-way flow model but less so in the 2-way flow model. Finally, costs of a direct link have a positive impact on the occurrence of (strict) Nash networks in the 1-way flow model but a negative impact in the 2-way flow model. In our discussion on possible explanations for these results we focus on strategic asymmetry and asymmetry with respect to payoffs. We find that the latter asymmetry, i.e., payoff inequity, plays an important role in the network formation process.

Common tax competition models suggest that welfare states will undercut each other's tax rate to attract taxpayers and keep welfare recipients at bay. This will lead to a zero-taxation outcome in the absence of migration costs or other barriers to migration. This paper develops a two-country framework with mobile altruistic taxpayers and immobile welfare recipients. It shows that under the assumption of taxpayers motivated by warm glow altruism, tax competition leads to unique pure strategy Nash equilibria in taxation which are different from zero given sufficiently strong altruistic preferences. If countries are asymmetric with respect to the number of welfare recipients, pure altruism and inequity aversion preferences support additional unique pure strategy Nash equilibria in which the country with the fewer poor attracts more taxpayers and sets higher taxes. This implies that rich countries may benefit from tax competition.

The basic model of the literature on self-enforcing international environmental agreements is a model of autarkic countries. We extend that model by international trade and investigate its impact on the performance of Nash coalitions and on their stability, in particular, in a general equilibrium framework. First we characterize the performance of coalitions and non-coalition countries with regard to emissions and welfare and compare business as usual with the coalition-fringe scenario. In qualitative terms, the results in our free-trade model turn out to be the same as in the basic model for quadratic functional forms. In our model with international trade countries influence the terms of trade with their choice of policy and they make strategic use of that terms-of-trade effect. We find, however, that in the quadratic version of our model - as in the basic model - stable coalitions consist of no more than two countries. Finally, we explore the outcome of trade liberalization by moving from autarky to free trade. Although the coalition steps up its mitigation effort, world emissions rise which may be referred to as a green paradox of trade liberalization. Trade liberalization turns out to be bad for the environment as well as for the coalition countries' welfare and the aggregate welfare of all countries; it reduces the range of profitable coalitions, and it even tends to hamper the formation of stable coalitions.

The paper provides a theoretical foundation for the empirical regularities observed in estimations of wage consequences of overeducation and undereducation. Workers with more education than required for their jobs are observed to suffer wage penalties relative to workers with the same education in jobs that only require their educational level. Similarly, workers with less education than required for their jobs earn wage rewards. These departures from the Mincer human capital earnings function can be explained by Nash bargaining between workers and employers. Under fairly mild assumptions, Nash bargaining predicts a wage penalty for overeducation and a wage reward for undereducation, and further predicts that the wage penalty will exceed the wage reward. This paper reviews the established empirical regularities and then provides Nash bargaining results that explain these regularities.

This paper analyzes efficient pricing at a congested airport dominated by a single firm. Unlike much of the previous literature, we combine a dynamic (bottleneck) model of congestion and a vertical structure model that explicitly considers the role of airlines and passengers. We show that when a Stackelberg leader interacts with a competitive fringe, charging the congestion toll that is derived for fully atomistic carriers to both leader and fringe yields the first-best outcome. This holds regardless of the leader's internalization of congestion in the unregulated equilibrium, and regardless of the assumed demand substitution pattern between firms. This result implies that the financial deficit under optimal pricing may be less severe than what earlier studies suggest. Finally, we show that there are various alternative toll regimes that also induce the welfare maximizing outcome, and therefore widen the set of choices for regulators.

In games with continuum strategy sets, we model a player’s uncertainty about another player’s strategy, as an atomless probability distribution over the other player’s strategy set. We call a strategy profile (strictly) robust to strategic uncertainty if it is the limit, as uncertainty vanishes, of some sequence (all sequences) of strategy profiles in which every player’s strategy is optimal under his or her uncertainty about the others. General properties of this robustness criterion are derived and it is shown that it is a refinement of Nash equilibrium when payoff functions are continuous. We apply the criterion to a class of Bertrand competition games. These are discontinuous games that admit a continuum of Nash equilibria. Our robustness criterion selects a unique Nash equilibrium, and this selection agrees with recent experimental findings.

The apparent ubiquity of progressive taxation in advanced democracies has animated research by political economists in the past decade, but little progress has been made in modeling political equilibria over tax policy when labor supply is elastic with respect to taxation. Here, we postulate an economy with two worker types (wage capacities), in which the unskilled are more numerous than the skilled. Preferences are quasi-linear in income and leisure. One political party represents each worker type. A tax policy is any feasible incentive-compatible menu of pre- and post-tax incomes from which each worker must choose. This policy space is three-dimensional. Workers vote stochastically. The equilibrium concept for political competition is party-unanimity Nash equilibrium (PUNE)—thus, parties are both vote-seeking and representative. The set of political equilibria is characterized. We prove that, if the class of unskilled workers is not too large (but greater than one-half), then there always exist equilibria in which a regressive tax policy wins. If, however, that class is sufficiently numerous, or inequality is sufficiently great, then the victory of a progressive policy is guaranteed in all equilibria.

We formulate a dynamic game model of trade in an exhaustible resource with a quantity-setting cartel. We compute the feedback Nash equilibrium and two Stackelberg equilibria under two different leadership scenarios: leadership by the strategic importing country, and leadership by the exporting cartel. We numerically show that as compared to the Nash equilibrium, both players are better off if the importing country is the leader. The follower is worse off if the exporting cartel is the leader. Among the three game-theoretic outcomes, the world welfare is highest under the importing country's leadership and lowest under the exporting country's leadership.

We propose an equilibrium concept, the Robust Nash equilibrium (RNE), that combines the best-reply rationality and the first mover invariance condition. The single-stage 2x2 symmetric information game G is transformed into sequential two-stage games with two sub-trees: STA has the row player starting and STB has the column player starting. A profile in G is robust if it is the strict SPNE of the two branches; it is ephemeral if it is not the SPNE of any branch. We show that every strict dominant strategy equilibrium of G is robust but not every strict Nash equilibrium of G is. We show further that every robust profile of G is always a strict Nash equilibrium of G. A Robust Nash equilibrium (RNE) of G is any robust profile of G. The RNE of G is unique. We show in particular that the payoff dominant strict Nash equilibrium of a coordination game G is RNE while the strictly payoff-dominated Nash equilibrium of G is ephemeral. The original Harsanyi-Selten preference for payoff dominance over risk dominance is supported by robustness without invoking collective rationality.

This paper provides four axioms that uniquely characterize the sequential Raiffa solution proposed by Raiffa (1951, 1953) for two-person bargaining games. Three of these axioms are standard and are shared by several popular bargaining solutions. They suffice to characterize these solutions on TU-bargaining games where they coincide. The fourth axiom is a weakening of Kalai's (1977) axiom of step-by-step negotiating and turns out to be sort of a dual condition to a weaker version of Nash's IIA-axiom that together with the three standard axioms suffices to characterize the Nash bargaining solution due to Nash (1950). A conclusion of this axiomatization is that in contrast to all other known bargaining solutions the sequential Raiffa solution does not represent just another kind of fairness or equity condition in addition to the three standard axioms but rather is determined by indefinite repeated application of the three standard axioms.

Social networks, be it on the internet or in real life, facilitate information flows. We model this by giving agents incentives to link with others and receive information through those links. We consider networks where agents have an incentive to confirm the information they receive from others. Our paper analyzes the social networks that are formed. We first study the existence of Nash equilibria and then characterize the set of strict Nash networks. Next, we characterize the set of strictly efficient networks and discuss the relationship between strictly efficient networks and strict Nash networks. Finally, we check the robustness of our results by allowing for heterogeneity among agents, possibility of bilateral deviations of agents, and decay in the network.

We prove the existence of strategically stable sets of pure-strategy Nash equilibria (and hence the existence of pure-strategy trembling-hand perfect equilibria) in potential games that admit an upper semicontinuous potential, and we show that generic potential games possess pure-strategy strictly perfect and essential equilibria. In addition, we provide a link between upper semicontinuity of a potential and conditions defined directly on the payoff functions of a potential game. Finally, we show that stable sets and (strictly) perfect equilibria are related to the set of maximizers of a potential, which refines the set of Nash equilibria. Specifically, the set of maximizers of a potential contains a strategically stable set of pure-strategy Nash equilibria (and hence a pure-strategy trembling-hand perfect equilibrium) and, for generic games, any maximizer of a potential is a pure-strategy strictly perfect and essential equilibrium.

This paper characterizes analytically the optimal tariff of a large one-sector economy with monopolistic competition and firm heterogeneity in general equilibrium, thereby extending the small-country results of Demidova and Rodriguez-Clare (JIE, 2009) and the homogeneous firms framework of Gros (JIE, 1987). The optimal tariff internalizes a markup distortion and a terms of trade externality. It is larger the higher the dispersion of firm-level productivities, and the bigger the country's relative size or relative average productivity. Furthermore, in the two-country Nash equilibrium, tariffs turn out to be strategic substitutes. Small or poor economies set lower Nash tariffs than large or rich ones. Lower transportation costs or smaller fixed market entry costs induce higher equilibrium tariffs and larger welfare losses relative to the case of zero tariffs. Similarly, cross-country productivity or size convergence increases the global welfare loss due to non-cooperative tariff policies. These results suggest that post WWII trends have increased the relative merits of the WTO.

We investigate the relationship between the inner core and asymmetric Nash bargaining solutions for n-person bargaining games with complete information. We show that the set of asymmetric Nash bargaining solutions for different strictly positive vectors of weights coincides with the inner core if all points in the underlying bargaining set are strictly positive. Furthermore, we prove that every bargaining game is a market game. By using the results of Qin (1993) we conclude that for every possible vector of weights of the asymmetric Nash bargaining solution there exists an economy that has this asymmetric Nash bargaining solution as its unique competitive payoff vector. We relate the literature of Trockel (1996, 2005) with the ideas of Qin (1993). Our result can be seen as a market foundation for every asymmetric Nash bargaining solution in analogy to the results on non-cooperative foundations of cooperative games.

We provide approximation results for Nash equilibria in possibly discontinuous games when payoffs and strategy sets are perturbed, and compare these conditions to those considered in the related literature. We then prove existence results for a new finitistic infinite-game generalization of Selten's [17] notion of perfection, and study some of its properties. The existence results, which rely on the approximation theorems, relate existing notions of perfection to the new specification.

Higher-dimensional symmetric games become of more and more importance for applied micro- and macroeconomic research. Standard approaches to uniqueness of equilibria have the drawback that they are restrictive or not easy to evaluate analytically. In this paper I provide some general but comparably simple tools to verify whether a symmetric game has a unique symmetric equilibrium or not. I distinguish between the possibility of multiple symmetric equilibria and asymmetric equilibria which may be economically interesting and is useful to gain further insights into the causes of asymmetric equilibria in symmetric games with higher-dimensional strategy spaces. Moreover, symmetric games may be used to derive some properties of the equilibrium set of certain asymmetric versions of the symmetric game. I further use my approach to discuss the relationship between stability and (in)existence of multiple symmetric equilibria. While there is an equivalence between stability, inexistence of multiple symmetric equilibria and the unimportance of strategic effects for the comparative statics, this relationship breaks down in higher dimensions. Stability under symmetric adjustments is a minimum requirement of a symmetric equilibrium for reasonable comparative statics of symmetric changes. Finally, I present an alternative condition for a symmetric equilibrium to be a local contraction which is more general than the conventional approach of diagonal dominance and yet simpler to evaluate than the eigenvalue condition of continuous adjustment processes.

The ability to accurately evaluate an employee would seem to be a key activity in managing Information Technology (IT). Yet, workers may engage in dishonest and misleading behavior, which distort the evaluation, a variation of organizational politics. Why would they do so? One hypothesis is that privilege-seeking, that is, managing one's managers (also called rentseeking, management relations, or organizational politics), can be used by a worker to misrepresent his actual contribution. These activities lead to a reduction in productivity and consequently to a loss of profits. Management may decrease the firm's losses by engaging in costly monitoring activities. It is paradoxical that a behavior with such negative consequences is tolerated. A model is developed to show that an organization should be composed of employees with different levels of productivity; moreover, it may be optimal for the organization to have some employees who are good at privilege-seeking activities, forcing the remaining workers to invest in productive activities. This contradicts existing theory that unequal compensation should be less motivating and the remaining workers less productive.

In a recent paper, Jäger, Metzger, and Riedel (2011) study communication games of common interest when signals are simple and types complex. They characterize strict Nash equilibria as so-called Voronoi languages that consist of Voronoi tesselations of the type set and Bayesian estimators on the side of receivers. In this note, we introduce conflicts of interest in the same setting. We characterize strict Nash equilibria as distorted Voronoi languages that use all messages. For large conflicts, such informative equilibria need not exist. If the bias is sufficiently small, however, these equilibria do exist. This establishes the robustness of the results in Jäger, Metzger, and Riedel (2011) to biased interests. We finally give examples of strict Nash equilibria, one of them using simulations to illustrate an equilibrium with many messages and non-uniformly distributed types.

This paper analyzes the setting of national patent policies in the global economy. In the standard model with free trade and social-welfare-maximizing governments à la Grossman and Lai (2004), cross-border positive policy externalities induce individual countries to select patent strengths that are weaker than is optimal from a global perspective. The paper introduces three new features to the analysis: trade barriers, firm heterogeneity in terms of productivity and political economy considerations in setting patent policies. The first two features (trade barriers interacting with firm heterogeneity) tend to reduce the size of cross-border externalities in patent protection and therefore make national IPR policies closer to the global optimum. With firm lobbying creating profit-bias of the government, it is even possible that the equilibrium strength of global patent protection is greater than the globally efficient level. Thus, the question of under-protection or not is an empirical one. Based on calibration exercises, we find that there would be global under-protection of patent rights when there is no international policy coordination. Furthermore, requiring all countries to harmonize their patent standards with the equilibrium standard of the most innovative country (the US) does not lead to global over-protection of patent rights.

We model a player's uncertainty about other player's strategy choices as probability distributions over their strategy sets. We call a strategy profile robust to strategic uncertainty if it is the limit, as uncertainty vanishes, of some sequence of strategy profiles in each of which every player's strategy is optimal under his or her uncertainty about the pthers. We apply this definition to Bertrand games with a continuum of equilibrium prices and show that our robustness criterion selects a unique Nash equilibrium price. This selection agrees with available experimental findings.

A game-theoretic framework that allows for explicitly randomized strategies is used to study the e ect of ambiguity aversion on equilibrium outcomes. The notions of "independent strategies" as well as of "common priors" are amended to render them applicable to games in which players lack probabilistic sophistication. Within this framework the equilibrium predictions of two player games with ambiguity averse and with ambiguity neutral players are observationally equivalent. This equivalence result does not extend to the case of games with more than two players. A translation of the concept of equilibrium in beliefs to the context of ambiguity aversion yields substantially di erent predictions – even for the case with just two players.

Common wisdom holds that the introduction of a non-binding minimum wage is irrelevant for actual wages and employment. Empirical and experimental research, however, has shown that the introduction of a minimum wage can raise even those wages that were already above the new minimum wage. In this paper, we analyze how these findings can be explained by theoretical wage bargaining models between unions and firms. While the Nash bargaining solution is unaffected by minimum wages below initially bargained wages, we show that such minimum wages can drive up wages – and be harmful to employment – when bargaining follows the Kalai-Smorodinsky solution.

We introduce tax competition for mobile labor into an optimal-taxation model with two skill levels. We analyze a symmetric subgame-perfect Nash equilibrium of the game between two governments and two taxpayer populations. Tax competition reduces the distortion from the informational asymmetry and increases employment of the less productive individuals. When countries are heterogeneous, this effect is more pronounced in the smaller country.

We consider a general class of imperfectly discriminating contests with privately informed players. We show that findings by Athey (2001) imply the existence of a Bayesian Nash equilibrium in monotone pure strategies.

This paper characterizes the set of equilibrium networks in the two-way flow model of network formation with small decay, and this for all increasing benefit functions of the players. We show that as long as the population is large enough, this set contains large- as well as small-diameter networks. For all benefit functions, the periphery-sponsored star is the most stable. When the marginal benefits of information are constant, all non-star networks are equally stable. With increasing marginal benefits of information, small-diameter networks in general tend to be more stable. However, with decreasing marginal benefits of information, large-diameter networks tend to be the most robust along with the periphery-sponsored star.

This paper studies the evolutionary stability of the unique Nash equilibrium of a first price sealed bid auction. It is shown that the Nash equilibrium is not asymptotically stable under payoff monotonic dynamics for arbitrary initial popu- lations. In contrast, when the initial population includes a continuum of strategies around the equilibrium, the replicator dynamic does converge to the Nash equilibrium. Simulations are presented for the replicator and Brown-von Neumann-Nash dynamics. They suggest that the convergence for the replicator dynamic is slow compared to the Brown-von Neumann-Nash dynamics.

We introduce a network formation model based on the idea that individuals engage in production (or decide to participate in an action) depending on the similar actions of the people they observe in the society. We differentiate from the classical models of participation by letting individuals to choose, non-cooperatively, which agents to observe. Observing behavior of others is a costly activity but provides benefits in terms of reduction in cost of production for the observing agent, which we take it as learning. In this non-cooperative setting we provide complete characterization of both Nash stable and socially efficient network configurations. We show that every society can admit a stable network. Moreover, typically there will be multiple stable configurations that will be available for a society. While all stable networks will not be efficient, we show that every efficient network will be stable.

Car owners are liable for property damage inflicted on other motorists. In most countries such liability must be insured by law. That law may favor expensive or heavy vehicles, prone to suffer or inflict large losses. This paper explores links between liability rules and vehicle choice. It presumes cooperative insurance, but non-cooperative acquisition of vehicles. Thus, the Nash equilibrium and its degree of efficiency depend on the liability regime.

Several authors have proposed staggered wage bargaining as a way to introduce sticky wages into search and matching models while preserving individual rationality. I evaluate the quantitative implications of such an approach. I feed through a series of estimated shocks from US data into a search and matching model with sticky prices and wages. I compare the implications of how the sticky wages enter into the hiring decision, and there seems to be a tradeoff between generating business cycle volatility and matching the lack of a long-run relationship between vacancy creation and inflation. With regard to wages, the sticky wage model unconditionally does a better job at matching wages than the flexible wage model.

We report experiments designed to test between Nash equilibria that are stable and unstable under learning. The 'TASP' (Time Average of the Shapley Polygon) gives a precise prediction about what happens when there is divergence from equilibrium under fictitious play like learning processes. We use two 4 x 4 games each with a unique mixed Nash equilibrium; one is stable and one is unstable under learning. Both games are versions of Rock-Paper-Scissors with the addition of a fourth strategy, Dumb. Nash equilibrium places a weight of 1/2 on Dumb in both games, but the TASP places no weight on Dumb when the equilibrium is unstable. We also vary the level of monetary payoffs with higher payoffs predicted to increase instability. We find that the high payoff unstable treatment differs from the others. Frequency of Dumb is lower and play is further from Nash than in the other treatments. That is, we find support for the comparative statics prediction of learning theory, although the frequency of Dumb is substantially greater than zero in the unstable treatments.

This paper characterizes the Nash equilibrium in a pay-as-bid (discriminatory), divisible-good, procurement auction. Demand by the auctioneer is uncertain as in the supply function equilibrium model. A closed form expression is derived. Existence of an equilibrium is ensured if the hazard rate of the perfectly inelastic demand is monotonically decreasing and sellers have non-decreasing marginal costs. Multiple equilibria can be ruled out for markets, for which the auctioneer’s demand exceeds suppliers’ capacity with a positive probability. The derived equilibrium can be used to model strategic bidding behaviour in pay-as-bid electricity auctions, such as the balancing mechanism of United Kingdom. Offer curves and mark-ups of the derived equilibrium are compared to results for the SFE of a uniform-price auction.

In this paper, we reexamine Eliaz's results (2002) of fault tolerant implementation on one hand and we extend theorems 1 and 2 of Doghmi and Ziad (2008 a) to bounded rationality environments, on the other. We identify weak versions of the k-no veto power condition, in conjunction with unanimity and variants of k-monotonicity, are sufficient for implementability in k- Fault Tolerant Nash equilibria (k-FTNE). In addition, these new conditions are stable by intersection which makes it possible to check directly the k - FTNE implementability of the social choice correspondences. We apply these results to exchange economies with single -peaked preferences, to finite allocation problems, and to equilibrium theory. Firstly, we note that our conditions are satisfied by all monotonic solutions contrary to Eliaz's results (2002). Secondly, in exchange economy when preferences are single-peaked, the k-monotonicity is sufficient for the k - FTNE implementation for the correspondences and both necessary and sufficient for the functions. However, the results are negatives for the no-monotonic solutions

We explore how outcomes of trade policy retaliation (Nash tariff games) are affected when trade simultaneously takes places geographically across countries and through time via financial intermediation. In such models deficits and surpluses in goods trade are endogenously determined, and retaliatory trade policy towards goods can affect these and monetary trade models show different retaliatory trade outcomes from conventional goods only models. We use a general equilibrium goods trade model which also captures trade through time in the form of inside money as used in macro literature on one good overlapping generations models. In this model the deficit or surplus of any country in goods trade is endogenous determined. Optimal trade policy differs from that in a conventional goods only trade model in that countries which run trade deficits in goods will have more strategic power through tariff policy (and surplus countries less) than in models with balanced trade. We calibrate such a model to China's trade with the rest of the world and explore two country tariff games using 2005 data. Results show the significant impacts on Nash outcomes of endogenizing the Chinese trade surplus in the model in this way.

This article provides an exact non-cooperative foundation of the sequential Raiffa solution for two person bargaining games. Based on an approximate foundation due to Myerson (1997) for any two-person bargaining game (S,d) an extensive form game G(S,d) is defined that has an infinity of weakly subgame perfect equilibria whose payoff vectors coincide with that of the sequential Raiffa solution of (S,d). Moreover all those equilibria share the same equilibrium path consisting of proposing the Raiffa solution and accepting it in the first stage of the game. By a modification of G(S,d) the analogous result is provided for subgame perfect equilibria. Finally, it is indicated how these results can be extended to implementation of a sequential Raiffa (solution based) social choice rule in subgame perfect equilibrium.

In developing societies, social norms typically ascribe differential weights to paternal, maternal and communal (or state) contributions to children's expenses. Individuals internalize these valuations. I examine a Cournot model of voluntary contribution to children's goods in a two-adult household, where both spouses may have marginal rates of substitution across paternal, maternal and communal contributions that differ from unity. I show that a conflict may exist between the interests of parents and those of children. Depending on the marginal rate of substitution between paternal and maternal contributions, a lump-sum redistribution from fathers to mothers may make children better off, but both parents worse off, or vice versa. Additional public contribution funded by a lump-sum tax on either parent may make children better off, but at the cost of both parents. Thus, proposals to redistribute income from fathers to mothers need to take into account socially valorized gendered asymmetries in parental roles. Furthermore, there may exist a conflict, instead of congruence, between women and their children.

The mainstream model of option pricing is based on an exogenously given process of price movements. The implication of this assumption is that price movements are not affected by actions of market participants. However, if we assume that there are indeed impacts on the price movements it no longer possible to apply the standard pricing models. As a result we need an approach explaining interdependent actions. Game theory is in a position to offer proper olutions. This paper applies game theoretic concepts to determine option prices. Consequently, both the option price and the underlying´s expiration price are endogenously determined.

We consider general two-sided matching markets, so-called matching with contracts markets as introduced by Hatfield and Milgrom (2005), and analyze (Maskin) monotonic and Nash implementable solutions. We show that for matching with contracts markets the stable correspondence is monotonic and implementable (Theorems 1 and 3). Furthermore, any solution that is Pareto efficient, individually rational, and monotonic is a supersolution of the stable correspondence (Theore m 2). In other words, the stable correspondence is the minimal solution that is Pareto efficient, individually rational, and implementable.

This paper investigates the effect of fiscal equalization on the efficiency properties of corporate income tax rates chosen by symmetric countries in a Nash tax competition game under the taxation principles of Separate Accounting and Formula Apportionment. Fiscal equalization ensures efficiency if the marginal transfer just reflects the fiscal and pecuniary externalities of tax rates. In contrast to previous studies, tax base equalization (Representative Tax System) does not satisfy this condition, but combining tax revenue and private income equalization does, regardless of which taxation principle is implemented. Under Formula Apportionment, tax base equalization is superior to tax revenue equalization if the wage income externality is sufficiently large.

We demonstrate that in simple 2 x 2 games (cumulative) prospect theory preferences can be evolutionarily stable, i.e. a population of players with prospect theory preferences can not be invaded by more rational players. This holds also if probability weighting is applied to the probabilities of mixed strategies. We also show that in a typical game with infinitely many strategies, the “war of attrition”, probability weighting is evolutionarily stable. Finally, we generalize to other notions of stability. Our results may help to explain why probability weighting is generally observed in humans, although it is not optimal in usual decision problems.

It is well known that non-renegotiable contracts with third parties may have an effect on the outcome of a strategic interaction and thus serve as a commitment device. We address this issue when contracts are renegotiable. More precisely, we analyze the equilibrium outcomes of twostage games with renegotiation-proof third-party contracts in relation to the equilibrium outcomes of the same game without contracts. We assume that one of the parties in the contractual relationship is unable to observe everything that happens in the game when played by the other party. This implies that contracts are incomplete and we show that such incompleteness restricts the set of equilibrium outcomes to a subset of Nash equilibrium outcomes of the game without contracts. Introducing renegotiation, in general, imposes further constraints and in some games implies that only subgame perfect equilibrium outcomes can be supported. However, there is a large class of games in which non-subgame perfect equilibriumoutcomes can also be supported, and hence, third-party contracts still have strategic implications even when they are renegotiable.

It is unlikely that husbands and wives always agree on exactly what public goods to buy. Nor do they necessarily agree on how many hours to work with obvious consequences for the household budget. We therefore model consumption and labor supply behavior of a couple in a non-cooperative setting by adopting a Nash approach. Using minimal assumptions, we prove that demand for public goods is characterized by three regimes. It is either determined by the preferences of one of the partners only (Husband Dictatorship or Wife Dictatorship), or by both spouses' preferences where a partner's influence depends on the spouses' relative wage rates (Split Might). These regimes imply a kinked nature of the couple's aggregate demand curves. By imposing more structure on the model, we can derive testable implications on observed demand for public goods and labor supply that allow testing the model against the standard unitary model where a couple behaves as a single decision maker. The model is applied to a sample drawn from the Consumer Expenditure Survey (CEX) whereby we explicitly focus on expenses on children's goods that act as a public good in the spouses' preferences. We find that for couples with two or three children the standard unitary model is strongly rejected in favor of our non-cooperative model. Moreover, it turns out that for the majority of these couples, there is a Wife Dictatorship in the sense that the spending pattern is according to her preferences.