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San Jego is a two-player game with perfect information. It is a variation of the games Clobber (2001) and Cannibal Clobber. Given is a rectangular board with black and white pieces on the cells. Multiple pieces which are stacked on each other are called towers. The piece on top of a tower indicates her owner. A move consists of picking an own tower and placing it completely on top of an adjacent tower. If both players can not move anymore, the game ends. Winner is the player with the highest tower. An upper bound for the state-space complexity of San Jego is determined. Furthermore, the game-tree complexity is approximated theoretically and numerically. For small board sizes, the optimal game-theoretic values are calculated and the advantage of the first move is determined. [ABSTRACT FROM AUTHOR]

Research on how autistic people are perceived by neurotypical people indicates that disclosing a diagnosis leads to a positive discriminatory bias; however, autobiographical autistic accounts indicate that diagnostic disclosure often results in negative discriminatory behavior. We report on an exploratory study to compare people's self-reported helping behavior with their actual helping behavior toward an assumed autistic collaborator. We led 255 participants to believe that they were interacting online with a real person to play Dyad3D, a maze navigation game where players must work together to open doors, and complete the levels. However, participants were actually playing with an artificial confederate (AC) that is programmed to behave the same way across all interactions. This design enabled us to manipulate the diagnostic status of the AC that participants received prior to collaboration across three conditions: no disclosure, dyslexia-disclosure, and autism-disclosure. We use this method to explore two research questions: (1) is Dyad3D viable in creating a simulated interaction that could deceive participants into believing they were collaborating with another human player online? and (2) what are the effects of disclosing an autism diagnosis on social perception and collaboration? Combined with a post-game questionnaire, we compared differences between diagnostic conditions and differences between self-reported behavior and actual behavior in the game. Our findings show that Dyad3D proved to be an efficient and viable method for creating a believable interaction (deception success rate >96%). Moreover, diagnostic disclosure of autism results in the AC being perceived as more intelligent and useful, but participants also perceived themselves to be more helpful toward the AC than they actually were. We evaluate the strengths and limitations of the current method and provide recommendations for future research. The source code for Dyad3D is freely available (CC-BY-NC 4.0) so that the study is reproducible and open to future adaptation. [ABSTRACT FROM AUTHOR]

The graph grabbing game is a two-player game on weighted connected graphs where all weights are non-negative. Two players, Alice and Bob, alternately remove a non-cut vertex from the graph (i.e., the resulting graph is still connected) and get the weight assigned to the vertex, where the starting player is Alice. Each player’s aim is to maximize his/her outcome when all vertices have been taken, and Alice wins the game if she gathered at least half of the total weight. Seacrest and Seacrest (2017) proved that Alice has a winning strategy for every weighted tree with even order, and conjectured that the same statement holds for every weighted connected bipartite graph with even order. In this paper, we prove that Alice wins the game on a type of a connected bipartite graph with even order called a K m , n -tree . [ABSTRACT FROM AUTHOR]

We extend the study of procedural fairness in three new directions. Firstly, we focus on lotteries determining the initial roles in a two-person game. One of the roles carries a potential advantage over the other. All the experimental literature has thus far focused on lotteries determining the final payoffs of a game. Secondly, we modify procedural fairness in a dynamic-i.e. over several repetitions of a game-as well as in a static-i.e. within a single game-sense. Thirdly, we analyse whether assigning individuals a minimal chance of achieving an advantaged position is enough to make them willing to accept substantially more inequality. We find that procedural fairness matters under all of these accounts. Individuals clearly respond to the degree of fairness in assigning initial roles, appraise contexts that are dynamically fair more positively than contexts that are not, and are generally more willing to accept unequal outcomes when they are granted a minimal opportunity to acquire the advantaged position. Unexpectedly, granting full equality of opportunity does not lead to the highest efficiency. [ABSTRACT FROM AUTHOR]

We propose a parameter optimization method for quest design of massive multiplayer online role playing games (MMORPGs). Our system consists of two techniques-selective sampling of user trajectory data and parameter optimization based on a genetic algorithm. Our system generates an optimized quest play path, which is difficult to estimate. It is useful for preventing over rewarding in MMORPG quest design. In practice, the suggested systems can be applied easily to any type of MMORPG with scalability, and will be useful for reducing the manual cost for MMORPG development. [ABSTRACT FROM AUTHOR]

We consider two-player zero-sum stochastic games on graphs with ω-regular winning conditions specified as parity objectives. These games have applications in the design and control of reactive systems. We survey the complexity results for the problem of deciding the winner in such games, and in classes of interest obtained as special cases, based on the information and the power of randomization available to the players, on the class of objectives and on the winning mode. On the basis of information, these games can be classified as follows: (a) partial-observation (both players have partial view of the game); (b) one-sided partial-observation (one player has partial-observation and the other player has complete-observation); and (c) complete-observation (both players have complete view of the game). The one-sided partial-observation games have two important subclasses: the one-player games, known as partial-observation Markov decision processes (POMDPs), and the blind one-player games, known as probabilistic automata. On the basis of randomization, (a) the players may not be allowed to use randomization (pure strategies), or (b) they may choose a probability distribution over actions but the actual random choice is external and not visible to the player (actions invisible), or (c) they may use full randomization. Finally, various classes of games are obtained by restricting the parity objective to a reachability, safety, Büchi, or coBüchi condition. We also consider several winning modes, such as sure-winning (i.e., all outcomes of a strategy have to satisfy the winning condition), almost-sure winning (i.e., winning with probability 1), limit-sure winning (i.e., winning with probability arbitrarily close to 1), and value-threshold winning (i.e., winning with probability at least ν, where ν is a given rational). [ABSTRACT FROM AUTHOR]

The Marinatto-Weber approach to quantum games is a straightforward way to apply the power of quantum mechanics to classical game theory. In the simplest case, the quantum scheme is that players manipulate their own qubits of a twoqubit state either with the identity 1 or the Pauli operator σx. However, such a simplification of the scheme raises doubt as to whether it could really reflect a quantum game. In this paper we put forward examples which may constitute arguments against the present form of the Marinatto-Weber scheme. Next, we modify the scheme to eliminate the undesirable properties of the protocol by extending the players' strategy sets. [ABSTRACT FROM AUTHOR]

William D. Hamilton famously stated that "human life is a many person game and not just a disjoined collection of two person games". However, most of the theoretical results in evolutionary game theory have been developed for two player games. In spite of a multitude of examples ranging from humans to bacteria, multi-player games have received less attention than pairwise games due to their inherent complexity. Such complexities arise from the fact that group interactions cannot always be considered as a sum of multiple pairwise interactions. Mathematically, multi-player games provide a natural way to introduce non-linear, polynomial fitness functions into evolutionary game theory, whereas pairwise games lead to linear fitness functions. Similarly, studying finite populations is a natural way of introducing intrinsic stochasticity into population dynamics. While these topics have been dealt with individually, few have addressed the combination of finite populations and multi-player games so far. We are investigating the dynamical properties of evolutionary multi-player games in finite populations. Properties of the fixation probability and fixation time, which are relevant for rare mutations, are addressed in well mixed populations. For more frequent mutations, the average abundance is investigated in well mixed as well as in structured populations. While the fixation properties are generalizations of the results from two player scenarios, addressing the average abundance in multi-player games gives rise to novel outcomes not possible in pairwise games. [ABSTRACT FROM AUTHOR]

For duopoly models, we analyse the concept of coarse correlated equilibrium using simple symmetric devices that the players choose to commit to in equilibrium. In a linear duopoly game, we prove that Nash-centric devices, involving a sunspot structure, are simple symmetric coarse correlated equilibria. Any small unilateral perturbation from such a structure fails to be an equilibrium. [ABSTRACT FROM AUTHOR]

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This paper introduces two variations of the Public Good Index (Holler, 1982) for games with a priori unions. The first one stresses the public good property which suggests that all members of a winning coalition derive equal power. The second variation follows earlier work on the integration of a priori unions (Owen, 1977 and 1982) and refers to essential subsets of an a priori union when allocating power shares. Axiomatic characterizations of both indices are discussed. Numerical examples, one of them taken from a political setting, illustrate the new power indices presented in this paper. [ABSTRACT FROM AUTHOR]

The article discusses the random-turn hex game, which involves two players who take turns placing stones of their respective colors on the hexagons of a rhombus-shaped hexagonal grid. It requires the players to toss a coin before each turn to decide who gets to place the next stone rather than alternating turns. Its optimal strategy is very simple and a player wins by completing a path connecting the two opposite sides of his or her color. Details about the description of random-turn selection games are provided.

We analyze a class of two-candidate voter participation games under complete information that encompasses as special cases certain public good provision games. We characterize the Nash equilibria of these games as stationary points of a non-linear programming problem, the objective function of which is a Morse function (onethat does not admit degenerate critical points) for almost all costs of participation. We use this fact to establish that, outside a closed set of measure zero of participation costs, all equilibria of these games are regular (an alternative to the result of De Sinopoli and Iannantuoni in Econ Theory 25(2):477–486, 2005). One consequence of regularity is that the equilibria of these games are robust to the introduction of (mild) incomplete information. Finally, we establish the existence of monotone Nash equilibria, such that players with higher participation cost abstain with (weakly) higher probability. [ABSTRACT FROM AUTHOR]

We explore exploits possible for cheating in real-time, multiplayer games for both client-server and serverless architectures. We offer the first formalization of cheating in online games and propose an initial set of strong solutions. We propose a protocol that has provable anti-cheating guarantees, is provably safe and live, but suffers a performance penalty. We then develop an extended version of this protocol, called asynchronous synchronization, which avoids the penalty, is serverless, offers provable anti-cheating guarantees, is robust in the presence of packet loss, and provides for significantly increased communication performance. This technique is applicable to common game features as well as clustering and cell-based techniques for massively multiplayer games. Specifically, we provide a zero-knowledge proof protocol so that players are within a specific range of each other, and otherwise have no notion of their distance. Our performance claims are backed by analysis using a simulation based on real game traces. [ABSTRACT FROM AUTHOR]

Motivated by an analysis of Abramsky-Jagadeesan games, the paper considers a categorical semantics for a polarized notion of two-player games, a semantics which has close connections with the logic of (finite cartesian) sums and products, as well as with the multiplicative structure of linear logic. In each case, the structure is polarized, in the sense that it will be modelled by two categories, one for each of two polarities, with a module structure connecting them. These are studied in considerable detail, and a comparison is made with a different notion of polarization due to Olivier Laurent: there is an adjoint connection between the two notions. [ABSTRACT FROM AUTHOR]

This paper reports an experiment that elicits subjects' initial responses to 16 dominance-solvable two-person guessing games. The structure is publicly announced except for varying payoff parameters, to which subjects are given free access. Varying the parameters allows very strong separation of the behavior implied by leading decision rules. Subjects' decisions and searches show that most subjects understood the games and sought to maximize payoffs, but many had simplified models of others' decisions that led to systematic deviations from equilibrium. The predictable component of their deviations is well explained by a structural nonequilibrium model of initial responses based on level-k thinking. (JEL C72, C92, D83). [ABSTRACT FROM AUTHOR]

The substantively rational value of the games studied in this paper does not help predict subject performance in the experiment at all. An accurate model must account for the cognitive ability of the people playing the game. This paper investigates whether the variation in measured rationality bounds is correlated with the probability of winning when playing against another person in games that exceed both players’ estimated rationality bound. Does seeing deeper into a game matter when neither player can see to the end of the game? Subjects with higher measured bounds win 63 percent of the time and the larger the difference the more frequently they win. [ABSTRACT FROM AUTHOR]

The standard approach in a biological two-player game is to assume both players choose their actions independently of one another, having no information about their opponent's action (simultaneous game). However, this approach is not realistic in some circumstances. In many cases, one player chooses his action first and then the second player chooses her action with information about his action (Stackelberg game). We compare these two games, which can be mathematically analyzed into two types, depending on the direction of the best response function (BRF) at the evolutionarily stable strategy in the simultaneous game (ESSsim). We subcategorize each type of game into two cases, depending on the change in payoff to one player, when both players are at the ESSsim, and the other player increases his action. Our results show that in cases where the BRF is decreasing at the ESSsim, the first player in the Stackelberg game receives the highest payoff, followed by both players in the simultaneous game, followed by the second player in the Stackelberg game. In these cases, it is best to be the first Stackelberg player. In cases where the BRF is increasing at the ESSsim, both Stackelberg players receive a higher payoff than players in a simultaneous game. In these cases, it is better for both players to play a Stackelberg game rather than a simultaneous game. However, in some cases the first Stackelberg player receives a higher payoff than the second Stackelberg player, and in some cases the opposite is true. [ABSTRACT FROM AUTHOR]

Using the strategy method (Selten, 1967, Beitra¨ge zur experimentellen Wirtschaftsforschung, pp. 136–168) we elicit subjects' strategies for playing any 2-person (3×3)-game with integer payoffs between 0 and 99. In each of 5 tournaments, every strategy pair plays 500 000 games. The frequency of pure strategy equilibrium play increases from 51% in the first to 74% in the last tournament, with the equilibria that maximize joint payoff being preferred when multiple exist. For games without pure equilibria, strategies are typically based on elements of the best-reply cascade: MAP (maximize the expected payoff against uniformly randomizing opponents), BR-MAP (best reply to MAP), and BR-BR-MAP (best reply to BR-MAP). [Copyright &y& Elsevier]

We show the incompatibility between the existence of stationary subgame perfect equilibria in Shaked''s game of cycling offers with exogenous breakdown and the behavior of players consistent with the Allais Paradox. Thus, the strategic support of the equally marginally bold solution presented in Burgos, Grant, and Kajii [2002. Games Econ. Behav. 38, 28–51] does not go beyond the two-person case. [Copyright &y& Elsevier]

This paper concerns infinitely repeated and undiscounted two-person non-zero-sum games of incomplete information on one side. Following an improvement on the proof of equilibrium existence, it establishes sufficient conditions for the existence of an equilibrium with payoffs superior to what the players would receive from observable deviation. To do this, we show that a no-where empty convex valued upper hemi-continuous correspondence from a compact metric space to a compact and convex subset of a Euclidean space can be approximated by Hausdorff-continuous convex valued correspondences that contain the original correspondence. This paper can be considered to be a first step toward a theory of equilibrium selection for these games. Examples are presented that show both the difficulty of and the desirability for stronger results than those presented here. [Copyright &y& Elsevier]

We consider a repeated 2-person 0-sum game with incomplete information about the pay-off matrix. Player I (maximizer) knows the real pay-off matrix but he is uncertain about the beliefs of his opponent. We show that in this case the Aumann-Maschler results on incomplete information on one side no longer hold. In particular such a game will not have a value in general, in spite of the fact that one player is fully informed about the state of nature. [ABSTRACT FROM AUTHOR]

In a repeated zero-sum two-person game with incomplete information on both sides, the asymptotic value is defined as v = lim[subn→∞V[subn] where V[subn] is the value of the game with n repetitions. It is shown here that v may be a transcendental number even for games in which all parameters defining the game are rational. This is in contrast to the situation in stochastic games where by the result of Bewley-Kohlberg [2] v is algebraic. This indicates a fundamental difference between stochastic games and repeated games with incomplete information. [ABSTRACT FROM AUTHOR]

The article discusses the Capture and Take away games, which require problem-solving strategies. In the Capture game, the first player moves from the single position at the top of the board to one of the positions in the top row. The two players move in horizontal and vertical patterns or to the top position. There are 9 markers placed in a line or a circle in the Take away game. A player may take away one or two markers next to each other and the player to take away the last marker wins.

The article offers information about the game called Jack and Jill. It is a game where the lucky player wins every time. A little bit of luck is what the player needs to win Jack and Jill, for in this game, no luck means no win. Materials for the game are the two wooden balls that would constantly tumble after each other and would eventually mount the very top of the hill without a broken crown.