Stochastic game

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

Cooperation Between Multiple Newsvendors with Warehouses

Abstract: This study considers a supply chain that consists of n retailers, each facing a newsvendor problem, and m warehouses. The retailers are supplied with a single product via some warehouses. In these warehouses, the ordered amounts of goods of these retailers become available after some lead time. At the time that the goods arrive at the warehouses, demand realizations are known by the retailers. The retailers can increase their expected joint profits if they can coordinate their orders and make allocations after demand realization. For this setting, we consider an associated cooperative game between the retailers. We show that this associated cooperative game has a nonempty core. Finally, we introduce a noncooperative game, where the retailers decide on their order quantities individually, and show that the set of payoff vectors resulting from strong Nash equilibria corresponds to the core of the associated cooperative game.

Non-cooperative multicast and facility location games

Abstract: We consider a multicast game with selfish non-cooperative players There is a special source node and each player is interested in connecting to the source by making a routing decision that minimizes its payment The mutual influence of the players is determined by a cost sharing mechanism, which in our case evenly splits the cost of an edge among the players using it We consider two different models: an integral model, where each player connects to the source by choosing a single path, and a fractional model, where a player is allowed to split the flow it receives from the source between several paths In both models we explore the overhead incurred in network cost due to the selfish behavior of the users, as well as the computational complexity of finding a Nash equilibriumThe existence of a Nash equilibrium for the integral model was previously established by the means of a potential function We prove that finding a Nash equilibrium that minimizes the potential function is NP-hard We focus on the price of anarchy of a Nash equilibrium resulting from the best-response dynamics of a game course, where the players join the game sequentially For a game with n players, we establish an upper bound of O(√n log2n) on the price of anarchy, and a lower bound of Ω(log n/ log log n) For the fractional model, we prove the existence of a Nash equilibrium via a potential function and give a polynomial time algorithm for computing an equilibrium that minimizes the potential function Finally, we consider a weighted extension of the multicast game, and prove that in the fractional model, the game always has a Nash equilibrium

Effects of expectation and noise on evolutionary games

Abstract: Considering the difference between the actual and expected payoffs, we bring a stochastic learning updating rule into an evolutionary Prisoners Dilemma game and the Snowdrift game on scale-free networks, and then investigate how the expectation level A and environmental noise κ influence cooperative behavior Interestingly, numerical results show that the mechanism of promoting cooperation exhibits a resonance-like fashion including the coaction of A , κ and the payoff parameters High cooperator frequency is induced by some optimal parameter regions The variation of time series has also been investigated This work could be of particular interest in the evolutionary game dynamics of biological and social systems

Effects of strategy-migration direction and noise in the evolutionary spatial prisoner's dilemma

Abstract: Spatial games are crucial for understanding patterns of cooperation in nature (and to some extent society). They are known to be more sensitive to local symmetries than, e.g., spin models. This paper concerns the evolution of the prisoner's dilemma game on regular lattices with three different types of neighborhoods\char22{}the von Neumann, Moore, and kagom\'e types. We investigate two kinds of dynamics for the players to update their strategies (that can be unconditional cooperator or defector). Depending on the payoff difference, an individual can adopt the strategy of a random neighbor [a voter-model-like dynamics (VMLD)] or impose its strategy on a random neighbor, i.e., invasion-process-like dynamics (IPLD). In particular, we focus on the effects of noise, in combination with the strategy dynamics, on the evolution of cooperation. We find that VMLD, compared to IPLD, better supports the spreading and sustaining of cooperation. We see that noise has nontrivial effects on the evolution of cooperation: maximum cooperation density can be realized either at a medium noise level, in the limit of zero noise or in both these regions. The temptation to defect and the local interaction structure determine the outcome. Especially, in the low noise limit, the local interaction plays a crucial role in determining the fate of cooperators. We elucidate these both by numerical simulations and mean-field cluster approximation methods.

Cyclic Markov equilibria in stochastic games

Abstract: We examine a three-person stochastic game where the only existing equilibria consist of cyclic Markov strategies. Unlike in two-person games of a similar type, stationary e-equilibria (e > 0) do not exist for this game. Besides we characterize the set of feasible equilibrium rewards.