198,165 research outputs found
Robust stochastic stability
A strategy profile of a game is called robustly stochastically stable if it is stochastically stable for a given behavioral model independently of the specification of revision opportunities and tie-breaking assumptions in the dynamics. We provide a simple radius-coradius result for robust stochastic stability and examine several applications. For the logit-response dynamics, the selection of potential maximizers is robust for the subclass of supermodular symmetric binary-action games. For the mistakes model, the weaker property of strategic complementarity suffices for robustness in this class of games. We also investigate the robustness of the selection of risk-dominant strategies in coordination games under best-reply and the selection of Walrasian strategies in aggregative games under imitation.Learning in games, stochastic stability, radius-coradius theorems, logit-response dynamics, mutations, imitation
Multiplicity and Sensitivity of Stochastically Stable Equilibria in Coordination Games
We investigate the equilibrium selection problem in n-person binary coordination games by means of the adaptive play with mistakes (Young 1993). We show that whenever the difference between the deviation losses of respective equilibria is not overwhelming, the stochastic stability exhibits a notable dependence on payoff parameters associated with strategy profiles where the numbers of players for the respective strategies are nearly equal. This feature necessitates the existence of games that possess multiple stochastically stable equilibria.Equilibrium selection, stochastic stability, unanimity game, coordination game
The Evolutionary Robustness of Forgiveness and Cooperation
We study the evolutionary robustness of strategies in infinitely repeated
prisoners' dilemma games in which players make mistakes with a small
probability and are patient. The evolutionary process we consider is given by
the replicator dynamics. We show that there are strategies with a uniformly
large basin of attraction independently of the size of the population.
Moreover, we show that those strategies forgive defections and, assuming that
they are symmetric, they cooperate
Multiple Stochastically Stable Equilibria in Coordination Games
In an (n,m)-coordination game, each of the n players has two alternative strategies. A strategy generates positive payoff only if there are at least m-1 others who choose the same, where m>n/2. The payoff is nondecreasing in the number of such others so that there are exactly two strict equilibria. Applying the adaptive play with mistakes (Young 1993) to (n,m)-coordination games, we point out potential complications inherent in many-person games. Focusing on games that admit simple analysis, we show that there is a nonempty open set of (n,m)-coordination games that possess multiple stochastically stable equilibria, which may be Pareto ranked, if and only if m>(n+3)/2, which in turn is equivalent to the condition that there is a strategy profile against which every player has alternative best responses.Equilibrium selection, stochastic stability, unanimity game, coordination game, collective decision making
Learning, Experimentation, and Long-Run Behavior in Games
This paper investigates a class of population-learning dynamics. In every period agents either adopt a best reply to the current distribution of actual play, or a best reply to a sample, taken with replacement, from the distribution of intended play (the strategies adopted at the end of last period), or they are inactive. If sampling with replacement and being inactive have strictly positive probability, these dynamics converge globally to minimal curb sets in the absence of mistakes. For two-player i x j-games, i; j .le. 3; the same result holds even if only best responding to actual play and being inactive have positive probability. If players make mistakes in the implementation of their strategies, these dynamics select among minimal curb sets .
Extensive-Form Perfect Equilibrium Computation in Two-Player Games
We study the problem of computing an Extensive-Form Perfect Equilibrium
(EFPE) in 2-player games. This equilibrium concept refines the Nash equilibrium
requiring resilience w.r.t. a specific vanishing perturbation (representing
mistakes of the players at each decision node). The scientific challenge is
intrinsic to the EFPE definition: it requires a perturbation over the agent
form, but the agent form is computationally inefficient, due to the presence of
highly nonlinear constraints. We show that the sequence form can be exploited
in a non-trivial way and that, for general-sum games, finding an EFPE is
equivalent to solving a suitably perturbed linear complementarity problem. We
prove that Lemke's algorithm can be applied, showing that computing an EFPE is
-complete. In the notable case of zero-sum games, the problem is
in and can be solved by linear programming. Our algorithms also
allow one to find a Nash equilibrium when players cannot perfectly control
their moves, being subject to a given execution uncertainty, as is the case in
most realistic physical settings.Comment: To appear in AAAI 1
A simple hybrid algorithm for improving team sport AI
In the very popular genre of team sports games defeating the opposing AI is the main focus of the gameplay experience. However the overall quality of these games is significantly damaged because, in a lot of cases, the opposition is prone to mistakes or vulnerable to exploitation. This paper introduces an AI system which overcomes this failing through the addition of simple adaptive learning and prediction algorithms to a basic ice hockey defence. The paper shows that improvements can be made to the gameplay experience without overly increasing the implementation complexity of the system or negatively affecting its performance. The created defensive system detects patterns in the offensive tactics used against it and changes elements of its reaction accordingly; effectively adapting to attempted exploitation of repeated tactics. This is achieved using a fuzzy inference system that tracks player movement, which greatly improves variation of defender positioning, alongside an N-gram pattern recognition-based algorithm that predicts the next action of the attacking player. Analysis of implementation complexity and execution overhead shows that these techniques are not prohibitively expensive in either respect, and are therefore appropriate for use in games
A Comment on "Cycles and Instability in a Rock-Paper-Scissors Population Game: A Continuous Time Experiment"
The authors (Cason, Friedman and Hopkins, Reviews of Economics Studies, 2014)
claimed a result that the treatments (using simultaneous matching in discrete
time) replicate previous results that exhibit weak or no cycles. After correct
two mathematical mistakes in their cycles tripwire algorithm, we research the
cycles by scanning the tripwire in the full strategy space of the games and we
find significant cycles missed by the authors. So we suggest that, all of the
treatments (using simultaneous matching in discrete time) exhibit significant
cycles.Comment: 2 pages, Keywords: experiments, cycles, mixed equilibrium, discrete
time. JEL numbers: C72, C73, C92, D8
Stochastically Stable Equilibria in Coordination Games with Multiple Populations
We investigate the equilibrium selection problem in n-person binary coordination games by means of adaptive play with mistakes (Young 1993). The size and the depth of a particular type of basins of attraction are found to be the main factors in determining the selection outcome. The main result shows that if a strategy has the larger basin of attraction, and if it is deep enough, then the strategy constitutes a stochastically stable equilibrium. The existence of games with multiple stochastically stable equilibria is an immediate consequence of the result. We explicitly address the qualitative difference between selection results in multi-dimensional stochastic evolution models and those in single dimensional models, and shed some light on the source of the difference.Equilibrium selection, stochastic stability, unanimity game, coordination game
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