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In combinatorial game theory, under normal play convention, all games are invertible, whereas only the empty game is invertible in misère play. For this reason, several restricted universes of games were studied, in which more games are invertible. Here, we study combinatorial games under misère play, in particular universes where no player would like to pass their turn. In these universes, we prove that having one extra condition makes all games become invertible. We then focus our attention on a specific quotient, called QZ, and show that all sums of universes whose quotient is QZ also have QZ as their quotient. [ABSTRACT FROM AUTHOR]

We consider a setting where one has to organize one or several group activities for a set of agents. Each agent will participate in at most one activity, and her preferences over activities depend on the number of participants in the activity. The goal is to assign agents to activities based on their preferences in a way that is socially optimal and/or stable. We put forward a general model for this setting, which is a natural generalization of anonymous hedonic games. We then focus on a special case of our model where agents’ preferences are binary, i.e., each agent classifies all pairs of the form ‘(activity, group size)’ into ones that are acceptable and ones that are not. We formulate several solution concepts for this scenario, and study them from the computational point of view, providing hardness results for the general case as well as efficient algorithms for settings where agents’ preferences satisfy certain natural constraints. [ABSTRACT FROM AUTHOR]

This paper considers the condition of perfect recall for the class of arbitrarily large discrete extensive form games. The known definitions of perfect recall are shown to be equivalent even beyond finite games. Further, a qualitatively new characterization in terms of choices is obtained. In particular, an extensive form game satisfies perfect recall if and only if the set of choices, viewed as sets of ultimate outcomes, fulfill the 'Trivial Intersection' property, that is, any two choices with nonempty intersection are ordered by set inclusion. [ABSTRACT FROM AUTHOR]

Experimental data for two types of bargaining games are used to study the role of strategic risk in the decision making process that takes place when subjects play a game only once. The bargaining games are the ultimatum game (UG) and the yes-or-no game (YNG). Strategic risk in a game stems from the effect on one player's payoff of the behavior of other players. In the UG this risk is high, while it is nearly absent in the YNG. In studying the decision making process of subjects we use the time elapsed before a choice is made (response time) as a proxy for amount of thought or introspection. We find that response times are on average larger in the UG than in the YNG, indicating a positive correlation between strategic risk and introspection. In both games the behavior of subjects with large response times is more dispersed than that of subjects with small response times. In the UG larger response time is associated with less generous and thus riskier behavior, while it is associated with more generous behavior in the YNG. [ABSTRACT FROM AUTHOR]

The general behavior of combinatorial scoring games is not well-understood. In this paper, we focus on a special class of 'well-tempered' scoring games. By analogy with Grossman and Siegel's notion of even- and odd-tempered normal play games, we declare a dicot scoring game to be even-tempered if all its options are odd-tempered, and odd-tempered if it is not atomic and all its options are even-tempered. Games of either sort are called well-tempered. These show up naturally when analyzing one of the 'knot games' introduced by Henrich et al. We consider disjunctive sums of well-tempered scoring games, and develop a theory for them analogous to the standard theory of disjunctive sums of normal play partizan games. We isolate a special class of inversive well-tempered games which behave like normal play partizan games or like the 'Milnor games' considered by Milnor and Hanner. In particular, inversive games (modulo equivalence) form a partially ordered abelian group, and there is an effective description of the partial order. Moreover, the full monoid of well-tempered scoring games (modulo equivalence) admits a complete description in terms of the group of inversive games. We also describe several examples of well-tempered scoring games and provide dictionaries listing the values of some small positions in two of these games. [ABSTRACT FROM AUTHOR]

Bonanno (Logics and the foundations of game and decision theory, Amsterdam University Press, Amsterdam, ) provides an epistemic characterization for the solution concept of iterated deletion of inferior strategy profiles (IDIP) by embedding strategic-form games with ordinal payoffs in non-probabilistic epistemic models which are built on Kripke frames. In this paper, we will follow the event-based approach to epistemic game theory and supplement strategic games with type space models, where each type is associated with a preference relation on the state space. In such a framework, IDIP can be characterized by the conditions that at least one player has correct beliefs about the state of the world and that there is common belief that every player is rational, has correct beliefs about the state of the world and has strictly monotone preferences. Moreover, we shall compare the epistemic motivations for IDIP and its mixed strategy variant known as strong rationalizability (SR). Presuppose the above conditions. Whenever there is also common belief that players' preferences are representable by some expected utility function IDIP still applies. But if there is common belief that players' preferences are representable by some expected payoff function, then SR results. [ABSTRACT FROM AUTHOR]

Most work in game theory assumes that players are perfect reasoners and have common knowledge of all significant aspects of the game. In earlier work (Halpern and Rêgo , arxiv.org/abs/0704.2014), we proposed a framework for representing and analyzing games with possibly unaware players, and suggested a generalization of Nash equilibrium appropriate for games with unaware players that we called generalized Nash equilibrium. Here, we use this framework to analyze other solution concepts that have been considered in the game-theory literature, with a focus on sequential equilibrium. [ABSTRACT FROM AUTHOR]

We examine the coalition-proof equilibria of a participation game in the provision of a (pure) public good. We study which Nash equilibria are achieved through cooperation, and we investigate coalition-proof equilibria under strict and weak domination. We show that under some incentive condition, (i) a profile of strategies is a coalition-proof equilibrium under strict domination if and only if it is a Nash equilibrium that is not strictly Pareto-dominated by any other Nash equilibrium and (ii) every strict Nash equilibrium for non-participants is a coalition-proof equilibrium under weak domination. [ABSTRACT FROM AUTHOR]

The study characterizes the position value and the Myerson value for communication situations. Each of these two values is represented by the Shapley value of a modified game obtained from the original communication situation. The difference between the two values comes from the existence of a coalition structure in the modified game. [ABSTRACT FROM AUTHOR]

We consider differential games with incomplete information. For special games with dynamics independent of the state of the system and linear payoffs, we give a representation formula for the value similar to the value of repeated games with lack of information on both sides. For general games, this representation formula does not hold and we introduce an approximation of the value: we build a sequence of functions converging to the value function. [ABSTRACT FROM AUTHOR]

case study of matching students with dormitory-groups at the Technion lead recently to the study of a variant of the stable matching model with a 'qualifying criterion' for the inclusion of a student among those getting an assignment. A notion of stability was introduced for the model and a (student-courting) algorithm which finds a matching that satisfied this criterion and has desired properties was described. Here, we show that students cannot benefit from misrepresenting preferences in an extension of the model that allows dormitory-groups to have different preferences over students and allows these preferences to be incomplete. [ABSTRACT FROM AUTHOR]

I analyze a stochastic bargaining game in which a renewable surplus is divided among n ≥ 5 committee members in each of an infinite number of periods, and the division implemented in one period becomes the status quo allocation of the surplus in the ensuing period. I establish existence of equilibrium exhibiting minimum winning coalitions, assuming sufficiently mild concavity of stage preferences. The analysis highlights the role of proposal power in committee deliberations and yields a fully strategic version of McKelvey's (J Econ Theory 12:472-482, 1976; Econometrica 47:1086-1112, 1979) dictatorial agenda setting. [ABSTRACT FROM AUTHOR]

The Shapley-Ichiishi result states that a game is convex if and only if the convex hull of marginal vectors equals the core. In this paper, we generalize this result by distinguishing equivalence classes of balanced games that share the same core structure. We then associate a system of linear inequalities with each equivalence class, and we show that the system defines the class. Application of this general theorem to the class of convex games yields an alternative proof of the Shapley-Ichiishi result. Other applications range from computation of stable sets in non-cooperative game theory to determination of classes of TU games on which the core correspondence is additive (even linear). For the case of convex games we prove that the theorem provides the minimal defining system of linear inequalities. An example shows that this is not necessarily true for other equivalence classes of balanced games. [ABSTRACT FROM AUTHOR]

We define and study games with upper bounds. In one of these games there are upper bounds on the possible payoffs for some coalitions. These restrictions require adjustments in the definitions of solution concepts. In the current paper we study the effect of the restrictions on the core and define and study the so-called truncated core. [ABSTRACT FROM AUTHOR]

Many public goods that are provided by coalitions have a group-size effect. Namely, people prefer to consume a public good in a larger coalition. This paper studies local public goods games with anonymous and separable group-size effect. The core is nonempty when coalition feasible sets are monotonic and players' preferences over public goods satisfy a condition called cardinal connectedness. Moreover, a core allocation consists of connected coalitions. [ABSTRACT FROM AUTHOR]

We consider an n-player bargaining problem where the utility possibility set is compact, convex, and stricly comprehensive. We show that a stationary subgame perfect Nash equilibrium exists, and that, if the Pareto surface is differentiable, all such equilibria converge to the Nash bargaining solution as the length of a time period between offers goes to zero. Without the differentiability assumption, convergence need not hold. [ABSTRACT FROM AUTHOR]

In the framework of the solution theory for cooperative transferable utility games, Hamiache axiomatized the well-known Shapley value as the unique one-point solution verifying the inessential game property, continuity, and associated consistency. The purpose of this paper is to extend Hamiache’s axiomatization to the class of efficient, symmetric, and linear values, of which the Shapley value is the most important representative. For this enlarged class of values, explicit relationships to the Shapley value are exploited in order to axiomatize such values with reference to a slightly adapted inessential game property, continuity, and a similar associated consistency. The latter axiom requires that the solutions of the initial game and its associated game (with the same player set, but a different characteristic function) coincide. [ABSTRACT FROM AUTHOR]

We study private-value auctions with n risk-averse bidders, where n is large. We first use asymptotic analysis techniques to calculate explicit approximations of the equilibrium bids and of the seller’s revenue in any k-price auction ( k = 1, 2, . . .). These explicit approximations show that in all large k-price auctions the effect of risk-aversion is O(1/ n2) small. Hence, all large k-price auctions with risk-averse bidders are O(1/ n2) revenue equivalent. The generalization, that all large auctions are O(1/ n2) revenue equivalent, is false. Indeed, we show that there exist auction mechanisms for which the limiting revenue as $${n\longrightarrow \infty }$$ with risk-averse bidders is strictly below the risk-neutral limit. Therefore, these auction mechanisms are not revenue equivalent to large k-price auctions even to leading-order as $${n\longrightarrow \infty }$$. [ABSTRACT FROM AUTHOR]

We study the existence of Nash equilibria in games with an infinite number of players. We show that there exists a Nash equilibrium in mixed strategies in all normal form games such that pure strategy sets are compact metric spaces and utility functions are continuous. The player set can be any nonempty set. [ABSTRACT FROM AUTHOR]

This article examines individual incentives to produce information on communication networks. In our setting, efforts are strategic complements along communication paths with convex decay. We analyze the relationship between efforts and centrality on a set of networks which are unambiguous in terms of ordinal centrality. We first show that in both dominant and dominated equilibria central agents exert more effort. Second, we explore the issue of social coordination induced by our game. [ABSTRACT FROM AUTHOR]

We study the problem of reaching a pure Nash equilibrium in multi-person games that are repeatedly played, under the assumption of uncoupledness: EVERY player knows only his own payoff function. We consider strategies that can be implemented by finite-state automata, and characterize the minimal number of states needed in order to guarantee that a pure Nash equilibrium is reached in every game where such an equilibrium exists. [ABSTRACT FROM AUTHOR]

The Shapley value of certain non-superadditive games appears in the Talmudic literature, and in the Talmud itself, in several different contexts. [ABSTRACT FROM AUTHOR]

Explicit formulas are given for the asymptotic value limλ → 0 v(λ) and the asymptotic minmax lim w(λ) of finite λ-discounted absorbing games together with new simple proofs for the existence of the limits as λ goes to zero. Similar characterizations for stationary Nash equilibrium payoffs are obtained. The results may be extended to absorbing games with compact metric action sets and jointly-continuous payoff functions. [ABSTRACT FROM AUTHOR]

This paper introduces the idea of dynamics in cooperative games. The concrete case of multi-stage sequencing situations and the difficulties involved in defining stable cost savings allocations for the games arising from these situations is studied. The MEGS-rule is defined and proven to yield stable allocations. A characterization for the MEGS-rule is given. [ABSTRACT FROM AUTHOR]

It is well known that any decision efficient, budget balanced, and envy-free mechanism for allocating a single object with transfers is vulnerable to manipulation. In this paper we examine whether the possible manipulations can have a serious impact on the outcome. Specifically, we examine which allocations are realized in the direct revelation game of any rule satisfying certain normative properties. For this class of rules we show that decision efficient, budget balanced, and envy-free allocations are the only ones realized through an ɛ-Nash equilibrium for any sufficiently small ɛ > 0. [ABSTRACT FROM AUTHOR]

In games with costly signaling, some equilibria are vulnerable to deviations which could be “unambiguously” interpreted as coming from a unique set of Sender-types. This occurs when these types are precisely the ones who gain from deviating for any beliefs the Receiver could form over that set. We show that this idea characterizes a unique equilibrium outcome in two classes of games. First, in monotonic signaling games, only the Riley outcome is immune to this sort of deviation. Our result therefore provides a plausible story behind the selection made by Cho and Kreps’s (Q J Econ 102:179–221, 1987) D1 criterion on this class of games. Second, we examine a version of Crawford and Sobel (Econometrica 50:1431–1451, 1982) model with costly signaling, where standard refinements have no effect. We show that only a Riley-like separating equilibrium is immune to these deviations. [ABSTRACT FROM AUTHOR]

The paper follows Kalai and Samet’s (Econometrica 53:307–327, 1985) construction to define a possible extension of the equal allocation of nonseparable costs (EANSC) to games without transferable utilities. We offer a characterization of the EANSC based on the axiom of independence of irrelevant monotonic transformation [Chang and Hwang (Int J Game Theory 32:253–271, 2003) introduced this axiom, and they named it independence of irrelevant expansions. The referee points out that the terminology is inappropriate. So, we change the name.] introduced by Chang and Hwang (Int J Game Theory 32:253–271, 2003) as well as on several familiar axioms. Specifically, we show that the EANSC is the only solution to satisfy Pareto optimality, translation covariance, anonymity, TU-bilateral consistency (or TU-converse consistency), aggregate monotonicity, and independence of irrelevant monotonic transformation. [ABSTRACT FROM AUTHOR]

We consider a demand bargaining model where the formateur (proposal maker) is appointed before the players state their demands. In a general continuous framework, we show that if the decision has a distributive dimension, then the formateur gets his way. [ABSTRACT FROM AUTHOR]

The continuously stable strategy (CSS) concept, originally developed as an intuitive static condition to predict the dynamic stability of a monomorphic population, is shown to be closely related to classical game-theoretic dominance criteria when applied to continuous strategy spaces. Specifically, for symmetric and non symmetric two-player games, a CSS in the interior of the continuous strategy space is equivalent to neighborhood half-superiority which, for a symmetric game, is connected to the half-dominance and/or risk dominance concepts. For non symmetric games where both players have a one-dimensional continuous strategy space, an interior CSS is shown to be given by a local version of dominance solvability (called neighborhood dominance solvable). Finally, the CSS and half-superiority concepts are applied to points in the bargaining set of Nash bargaining problems. [ABSTRACT FROM AUTHOR]

An information structure in a non-cooperative game determines the signal that each player observes as a function of the strategy profile. Such information structure is called non-manipulable if no player can gain new information by changing his strategy. A Conjectural Equilibrium (CE) (Battigalli in Unpublished undergraduate dissertation, 1987; Battigalli and Guaitoli 1988; Decisions, games and markets, 1997) with respect to a given information structure is a strategy profile in which each player plays a best response to his conjecture about his opponents’ play and his conjecture is not contradicted by the signal he observes. We provide a sufficient condition for the existence of pure CE in games with a non-manipulable information structure. We then apply this condition to prove existence of pure CE in two classes of games when the information that players have is the distribution of strategies in the population. [ABSTRACT FROM AUTHOR]

New characterizations of sequential equilibrium, perfect equilibrium, and proper equilibrium are provided that use nonstandard probability. It is shown that there exists a belief system μ such that $${(\vec{\sigma},\mu)}$$ is a sequential equilibrium in an extensive game with perfect recall iff there exist an infinitesimal $${\epsilon}$$ and a completely mixed behavioral strategy profile σ′ (so that $${\sigma_i'}$$ assigns positive, although possibly infinitesimal, probability to all actions at every information set) that differs only infinitesimally from $${\vec{\sigma}}$$ such that at each information set I for player i, σ i is an $${\epsilon}$$-best response to $${\vec{\sigma}'_{-i}}$$ conditional on having reached I. Note that the characterization of sequential equilibrium does not involve belief systems. There is a similar characterization of perfect equilibrium; the only difference is that σ i must be a best response to $${\vec{\sigma}'_{-i}}$$ conditional on having reached I. Yet another variant is used to characterize proper equilibrium. [ABSTRACT FROM AUTHOR]

Treating games of incomplete information, we demonstrate that the existence of an ex post stable strategy vector implies the existence of an approximate Bayesian equilibrium in pure strategies that is also expost stable. Through examples we demonstrate the ‘bounds obtained on the approximation’ are tight. [ABSTRACT FROM AUTHOR]

Classical cooperative game theory is no longer a suitable tool for those situations where the values of coalitions are not known with certainty. We consider a dynamic context where at each point in time the coalitional values are unknown but bounded by a polyhedron. However, the average value of each coalition in the long run is known with certainty. We design “robust” allocation rules for this context, which are allocation rules that keep the coalition excess bounded while guaranteeing each player a certain average allocation (over time). We also present a joint replenishment application to motivate our model. [ABSTRACT FROM AUTHOR]

We consider the problem of allocating houses to agents when monetary compensations are not allowed. We present a simple and independent proof of a result due to Ehlers and Klaus (Int J Game Theory 32:545–560, 2004) that characterizes the class of rules satisfying efficiency, strategy-proofness, resource monotonicity and nonbossiness. [ABSTRACT FROM AUTHOR]

Suppose that individual payoffs depend on the network connecting them. Consider the following simultaneous move game of network formation: players announce independently the links they wish to form, and links are formed only under mutual consent. We provide necessary and sufficient conditions on the network link marginal payoffs such that the set of pairwise stable, pairwise-Nash and proper equilibrium networks coincide, where pairwise stable networks are robust to one-link deviations, while pairwise-Nash networks are robust to one-link creation but multi-link severance. Under these conditions, proper equilibria in pure strategies are fully characterized by one-link deviation checks. [ABSTRACT FROM AUTHOR]

A family of core extensions for cooperative TU-games is introduced. These solution concepts are non-empty when applied to non-balanced games yet coincide with the core whenever the core is non-empty. The extensions suggest how an exogenous regulator can sustain a stable and efficient outcome, financing a subsidy via individual taxes. Economic and geometric properties of the solution concepts are studied. When taxes are proportional, the proportional prenucleolus is proposed as a single-valued selection device. An application of these concepts to the decentralization of a public goods economy is discussed. [ABSTRACT FROM AUTHOR]

A popular approach to explain over-contribution in public good games is based on the assumption that people care (either positively or negatively) about the utility of other participants. Over-contribution then is an outcome of utility maximization where utility depends on subjects’ own payoffs as well as on the payoffs of other players. In this paper, I study to what extent this assumption of utility interdependence is responsible for over-contribution. I design three treatments where subjects’ decisions cannot affect opponents’ payoffs and thus utility interdependence cannot explain cooperative behavior. The main result is that while average contribution in these treatments is below the benchmark it nonetheless stays well above zero. Even when no one benefits from subjects’ generosity the average contributions are as high as one third of the endowment and are only 25% below those in the benchmark level. This suggests that utility interdependence is not the main factor responsible for over-contribution. [ABSTRACT FROM AUTHOR]

We demonstrate that, if there are sufficiently many players, any Bayesian equilibrium of an incomplete information game can be “ ε-purified” . That is, close to any Bayesian equilibrium there is an approximate Bayesian equilibrium in pure strategies. Our main contribution is obtaining this result for games with a countable set of pure strategies. In order to do so we derive a mathematical result, in the spirit of the Shapley–Folkman Theorem, permitting countable strategy sets. Our main assumption is a “large game property,” dictating that the actions of relatively small subsets of players cannot have large affects on the payoffs of other players. [ABSTRACT FROM AUTHOR]

In Tijs et al. (Eur J Oper Res 175:121–134, 2006) a new family of cost allocation rules is introduced in the context of cost spanning tree problems. In this paper we provide the first characterization of this family by means of population monotonicity and a property of additivity. [ABSTRACT FROM AUTHOR]

This paper studies two classical solution concepts for the structure of bicooperative games. First, we define the core and the Weber set of a bicooperative game and prove that the core is always contained in the Weber set. Next, we introduce a special class of bicooperative games, the so-called bisupermodular games, and show that these games are the only ones in which the core and the Weber set coincide. [ABSTRACT FROM AUTHOR]

This paper reinterprets the γ-core (Chander and Tulkens in Int Tax Pub Financ 2:279–293, 1995; in Int J Game Theory 26:379–401, 1997) and justifies it as well as its prediction that the efficient coalition structure is stable in terms of the coalition formation theory. The problem of coalition formation is formulated as an infinitely repeated game in which the players must choose whether to cooperate or not. It is shown that a certain equilibrium of this game corresponds to the γ-core assumption that when a coalition forms the remaining players form singletons, and that the grand coalition is an equilibrium coalition structure. [ABSTRACT FROM AUTHOR]

We propose a two-person game-theoretical model to study information sharing decisions at an interim stage when information is incomplete. The two agents have pieces of private information about the state of nature, and that information is improved by combining the pieces. Agents are both senders and receivers of information. There is an institutional arrangement that fixes a transfer of wealth from an agent who lies about her private information. In our model, we show that (1) there is a positive relation between information revelation and the amount of the transfers, and (2) information revelation has a collective action structure, in particular, the incentives of an agent to reveal decrease with respect to the amount of information disclosed by the other. [ABSTRACT FROM AUTHOR]

We study the cores of non-atomic market games, a class of transferable utility cooperative games introduced by Aumann and Shapley (Values of non-atomic games, 1974), and, more in general, of those games that admit a na-continuous and concave extension to the set of ideal coalitions, studied by Einy et al. (Int J Game Theory 28:1-14, 1999). We show that the core of such games is norm compact and some related results. We also give a Multiple Priors interpretation of some of our findings. [ABSTRACT FROM AUTHOR]

We examine a variety of stability and equilibrium definitions that have been used to study the formation of social networks among a group of players. In particular we compare variations on three types of definitions: those based on a pairwise stability notion, those based on the Nash equilibria of a link formation game, and those based on equilibria of a link formation game where transfers are possible. [ABSTRACT FROM AUTHOR]

In this paper we experimentally investigate Cournot duopolies with an extended timing game. The timing game has observable delay, that is, firms announce a production period (one out of two periods) and then they produce in the announced sequence. Theory predicts simultaneous production in the first period. With random matching we find that, given the actual experimental behavior in the subgames, subjects play a timing game more akin to a coordination game with two symmetric equilibria rather than the predicted game with a dominant strategy to produce early. As a result, a substantial proportion of subjects choose the second period. [ABSTRACT FROM AUTHOR]

We study the effect of asynchronous choice structure on the possibility of cooperation in repeated strategic situations. We model the strategic situations as asynchronously repeated games, and define two notions of effective minimax value. We show that the order of players’ moves generally affects the effective minimax value of the asynchronously repeated game in significant ways, but the order of moves becomes irrelevant when the stage game satisfies the non-equivalent utilities (NEU) condition. We then prove the Folk Theorem that a payoff vector can be supported as a subgame perfect equilibrium outcome with correlation device if and only if it dominates the effective minimax value. These results, in particular, imply both Lagunoff and Matsui’s (1997) result and Yoon (2001)’s result on asynchronously repeated games. [ABSTRACT FROM AUTHOR]

It is well known that the set of correlated equilibrium distributions of an n-player noncooperative game is a convex polytope that includes all the Nash equilibrium distributions. We demonstrate an elementary yet surprising result: the Nash equilibria all lie on the boundary of the polytope. [ABSTRACT FROM AUTHOR]

Three solution concepts for cooperative games with random payoffs are introduced. These are the marginal value, the dividend value and the selector value. Inspiration for their definitions comes from several equivalent formulations of the Shapley value for cooperative TU games. An example shows that the equivalence is not preserved since these solutions can all be different for cooperative games with random payoffs. Properties are studied and a characterization on a subclass of games is provided. [ABSTRACT FROM AUTHOR]

We provide a direct proof of a representation theorem for additive cost sharing methods as sums of path methods. Also, by directly considering the paths that generate some common additive cost sharing methods (Aumann-Shapley, Shapley Shubik, and Serial Cost) we show that they are consistent. These results follow directly from a simple sufficient condition for consistency: being generated by an associative path. We also introduce a new axiom, dummy consistency, which is quite mild. Using this, we also show that the Aumann-Shapley and Serial Cost methods are the unique (additive) consistent extension of their restriction on all two agent problems, while the Shapley-Shubik method has multiple consistent extensions but a unique anonymous scale invariant one. [ABSTRACT FROM AUTHOR]

We revisit n-player coordination games with Pareto-ranked Nash equilibria. As a novelty, we introduce fuzzy play and a matching device. By fuzzy play we mean that each player does not choose which pure strategy to play, but instead chooses a nonempty subset of his strategy set that he submits to the matching device. The matching device is a very simple one. It randomly selects a match if possible, and it selects randomly some strategy belonging to the strategy set sent by each player otherwise. That is, it does not impose that the best alternatives are matched. Using the concepts of perfect Nash equilibrium and of trembling-hand perfect rationalizability, we show that players coordinate directly on the Pareto optimal outcome. This implies that they neither use the option of fuzzy play, nor make use of the matching device. [ABSTRACT FROM AUTHOR]