General-sum stochastic games: Verifiability conditions for Nash equilibria

Unlike zero-sum stochastic games, a difficult problem in general-sum stochastic games is to obtain verifiable conditions for Nash equilibria. We show in this paper that by splitting an associated non-linear optimization problem into several sub-problems, characterization of Nash equilibria in a general-sum discounted stochastic games is possible. Using the aforementioned sub-problems, we in fact derive a set of necessary and sufficient verifiable conditions (termed KKT-SP conditions) for a strategy-pair to result in Nash equilibrium. Also, we show that any algorithm which tracks the zero of the gradient of the Lagrangian of every sub-problem provides a Nash strategy-pair. (c) 2012 Elsevier Ltd. All rights reserved.

Spatial SINR Games of Base Station Placement and Mobile Association

We study the question of determining locations of base stations (BSs) that may belong to the same or to competing service providers. We take into account the impact of these decisions on the behavior of intelligent mobile terminals that can connect to the base station that offers the best utility. The signal-to-interference-plus-noise ratio (SINR) is used as the quantity that determines the association. We first study the SINR association-game: We determine the cells corresponding to each base stations, i.e., the locations at which mobile terminals prefer to connect to a given base station than to others. We make some surprising observations: 1) displacing a base station a little in one direction may result in a displacement of the boundary of the corresponding cell to the opposite direction; 2) a cell corresponding to a BS may be the union of disconnected subcells. We then study the hierarchical equilibrium in the combined BS location and mobile association problem: We determine where to locate the BSs so as to maximize the revenues obtained at the induced SINR mobile association game. We consider the cases of single frequency band and two frequency bands of operation. Finally, we also consider hierarchical equilibria in two frequency systems with successive interference cancellation.

Zero-sum risk-sensitive stochastic games on a countable state space

Infinite horizon discounted-cost and ergodic-cost risk-sensitive zero-sum stochastic games for controlled Markov chains with countably many states are analyzed. Upper and lower values for these games are established. The existence of value and saddle-point equilibria in the class of Markov strategies is proved for the discounted-cost game. The existence of value and saddle-point equilibria in the class of stationary strategies is proved under the uniform ergodicity condition for the ergodic-cost game. The value of the ergodic-cost game happens to be the product of the inverse of the risk-sensitivity factor and the logarithm of the common Perron-Frobenius eigenvalue of the associated controlled nonlinear kernels. (C) 2013 Elsevier B.V. All rights reserved.

Zero-Sum Stochastic Games with Partial Information and Average Payoff

We consider a discrete time partially observable zero-sum stochastic game with average payoff criterion. We study the game using an equivalent completely observable game. We show that the game has a value and also we present a pair of optimal strategies for both the players.

Nonlinear Differential Games-Based Impact-Angle-Constrained Guidance Law

The problem of intercepting a maneuvering target at a prespecified impact angle is posed in nonlinear zero-sum differential games framework. A feedback form solution is proposed by extending state-dependent Riccati equation method to nonlinear zero-sum differential games. An analytic solution is obtained for the state-dependent Riccati equation corresponding to the impact-angle-constrained guidance problem. The impact-angle-constrained guidance law is derived using the states line-of-sight rate and projected terminal impact angle error. Local asymptotic stability conditions for the closed-loop system corresponding to these states are studied. Time-to-go estimation is not explicitly required to derive and implement the proposed guidance law. Performance of the proposed guidance law is validated using two-dimensional simulation of the relative nonlinear kinematics as well as a thrust-driven realistic interceptor model.

Necessary and sufficient conditions for optimality in constrained general sum stochastic games

In this paper we first derive a necessary and sufficient condition for a stationary strategy to be the Nash equilibrium of discounted constrained stochastic game under certain assumptions. In this process we also develop a nonlinear (non-convex) optimization problem for a discounted constrained stochastic game. We use the linear best response functions of every player and complementary slackness theorem for linear programs to derive both the optimization problem and the equivalent condition. We then extend this result to average reward constrained stochastic games. Finally, we present a heuristic algorithm motivated by our necessary and sufficient conditions for a discounted cost constrained stochastic game. We numerically observe the convergence of this algorithm to Nash equilibrium. (C) 2015 Elsevier B.V. All rights reserved.

Unraveling Public Good Games: The Role of Priors

This paper provides experimental evidence on how players predict end game effects in a linear public good game. Our regression analysis yields a measure of the relative importance of priors and signals on subjects\' beliefs on contributions and allow us to conclude that, firstly, the weight of the signal is relatively unimportant, while priors have a large weight and, secondly, priors are the same for all periods. Hence, subjects do not expect end game effects and there is very little updating of beliefs.

On monotonic core allocations for coalitional games whith veto players

We characterize a monotonic core concept defined on the class of veto balanced games. We also discuss what restricted versions of monotonicity are possible when selecting core allocations. We introduce a family of monotonic core concepts for veto balanced games and we show that, in general, the nucleolus per capita is not monotonic.

The Supercore for Normal Form Games

We study the supercore of a system derived from a normal form game. For the case of a finite game with pure strategies, we define a sequence of games and show that the supercore of that system coincides with the set of Nash equilibrium strategy profiles of the last game in the sequence. This result is illustrated with the characterization of the supercore for the n-person prisoners’ dilemma. With regard to the mixed extension of a normal form game, we show that the set of Nash equilibrium profiles coincides with the supercore for games with a finite number of Nash equilibria. For games with an infinite number of Nash equilibria this need not be no longer the case. Yet, it is not difficult to find a binary relation which guarantees the coincidence of these two sets.

Replicator Dynamics and Evolutionary Stable Strategies in Heterogeneous Games

We generalise and extend the work of Iñarra and Laruelle (2011) by studying two person symmetric evolutionary games with two strategies, a heterogenous population with two possible types of individuals and incomplete information. Comparing such games with their classic homogeneous version vith complete information found in the literature, we show that for the class of anti-coordination games the only evolutionarily stable strategy vanishes. Instead, we find infinite neutrally stable strategies. We also model the evolutionary process using two different replicator dynamics setups, each with a different inheritance rule, and we show that both lead to the same results with respect to stability.

Games with perceptions

We assume that 2 x 2 matrix games are publicly known and that players perceive a dichotomous characteristic on their opponents which defines two types for each player. In turn, each type has beliefs concerning her opponent's types, and payoffs are assumed to be type-independent. We analyze whether the mere possibility of different types playing different strategies generates discriminatory equilibria. Given a specific information structure we find that in equilibrium a player discriminates between her types if and only if her opponent does so. We also find that for dominant solvable 2x2 games no discriminatory equilibrium exists, while under different conditions of concordance between players' beliefs discrimination appears for coordination and for competitive games. A complete characterization of the set of Bayesian equilibria is provided.

The von Neumann-Morgenstern stable sets for 2x2 games

We analyze the von Neumann and Morgenstern stable sets for the mixed extension of 2 2 games when only single profitable deviations are allowed. We show that the games without a strict Nash equilibrium have a unique vN&M stable set and otherwise they have infinite sets.

Learning in Network Games

We report the findings of an experiment designed to study how people learn and make decisions in network games. Network games offer new opportunities to identify learning rules, since on networks (compared to e.g. random matching) more rules differ in terms of their information requirements. Our experimental design enables us to observe both which actions participants choose and which information they consult before making their choices. We use this information to estimate learning types using maximum likelihood methods. There is substantial heterogeneity in learning types. However, the vast majority of our participants' decisions are best characterized by reinforcement learning or (myopic) best-response learning. The distribution of learning types seems fairly stable across contexts. Neither network topology nor the position of a player in the network seem to substantially affect the estimated distribution of learning types.

A monotonic core concept for convex games: The SD-prenucleolus

We prove that the SD-prenucleolus satisfies monotonicity in the class of convex games. The SD-prenucleolus is thus the only known continuous core concept that satisfies monotonicity for convex games. We also prove that for convex games the SD-prenucleolus and the SD-prekernel coincide.

Playing games with words cultural transfer in David Lynch's Blue Velvet

Eguíluz, Federico; Merino, Raquel; Olsen, Vickie; Pajares, Eterio; Santamaría, José Miguel (eds.)