Stochastic game

About: Stochastic game is a research topic. Over the lifetime, 9493 publications have been published within this topic receiving 202664 citations.

Meet Your Expectations With Guarantees: Beyond Worst-Case Synthesis in Quantitative Games

Abstract: We extend the quantitative synthesis framework by going beyond the worst-case. On the one hand, classical analysis of two-player games involves an adversary (modeling the environment of the system) which is purely antagonistic and asks for strict guarantees. On the other hand, stochastic models like Markov decision processes represent situations where the system is faced to a purely randomized environment: the aim is then to optimize the expected payoff, with no guarantee on individual outcomes. We introduce the beyond worst-case synthesis problem, which is to construct strategies that guarantee some quantitative requirement in the worst-case while providing an higher expected value against a particular stochastic model of the environment given as input. This problem is relevant to produce system controllers that provide nice expected performance in the everyday situation while ensuring a strict (but relaxed) performance threshold even in the event of very bad (while unlikely) circumstances. We study the beyond worst-case synthesis problem for two important quantitative settings: the mean-payoff and the shortest path. In both cases, we show how to decide the existence of finite-memory strategies satisfying the problem and how to synthesize one if one exists. We establish algorithms and we study complexity bounds and memory requirements.

On the Inefficiency Ratio of Stable Equilibria in Congestion Games

Abstract: Price of anarchy and price of stability are the primary notions for measuring the efficiency (i.e. the social welfare) of the outcome of a game. Both of these notions focus on extreme cases: one is defined as the inefficiency ratio of the worst-case equilibrium and the other as the best one. Therefore, studying these notions often results in discovering equilibria that are not necessarily the most likely outcomes of the dynamics of selfish and non-coordinating agents. The current paper studies the inefficiency of the equilibria that are most stable in the presence of noise. In particular, we study two variations of non-cooperative games: atomic congestion games and selfish load balancing. The noisy best-response dynamics in these games keeps the joint action profile around a particular set of equilibria that minimize the potential function. The inefficiency ratio in the neighborhood of these "stable" equilibria is much better than the price of anarchy. Furthermore, the dynamics reaches these equilibria in polynomial time. Our observations show that in the game environments where a small noise is present, the system as a whole works better than what a pessimist may predict. They also suggest that in congestion games, introducing a small noise in the payoff of the agents may improve the social welfare.

How sensitive are bargaining outcomes to changes in disagreement payoffs

Abstract: We use a human-subjects experiment to investigate how bargaining outcomes are affected by changes in bargainers’ disagreement payoffs Subjects bargain against changing opponents, with randomly drawn asymmetric disagreement outcomes that vary over plays of the game, and with complete information about disagreement payoffs and the cake size We find that subjects only respond about half as much as theoretically predicted to changes in their own disagreement payoff and to changes in their opponent’s disagreement payoff This effect is observed in a standard Nash demand game and a related unstructured bargaining game, in both early and late rounds, and is robust to moderate changes in stake sizes We show theoretically that standard models of expected utility maximisation are unable to account for this under-responsiveness, even when generalised to allow for risk aversion We also show that quantal-response equilibrium has, at best, mixed success in characterising our results However, a simple model of other-regarding preferences can explain our main results

Enhancement of cooperation in prisoner’s dilemma game on weighted lattices

Abstract: We introduce the vertex weight into the spatial prisoners’ dilemma game to investigate the evolution of cooperation. Each player on a square lattice is assigned to a particular weight followed by three types of distributions, which include the exponential, power-law and uniform ones. Compared with the traditional version, we find that the cooperation level is markedly enhanced under the weighted square lattice. For most ranges of b , the highest cooperation level can be obtained under the uniform distribution, while power-law distribution usually leads to the lowest cooperation. The distributed weight can produce a heavy heterogeneity among the individuals’ payoff, some cooperators with higher weight will foster the cooperative clusters and even spread the cooperation strategy around the clusters, while defectors have no such advantages. In addition, we still investigate the impact of the amplitude of undulation of weight distribution on the cooperation, and the non-monotonic behavior about b is observed. Finally, the influence of noise on the cooperation is also studied for these types of distribution of weight. To some extent, our weighted scheme can characterize the difference or diversity of players, which will be beneficial to further understand the role of individuals during the evolution of cooperation.