Related papers: A note on contests with a constrained choice set o…
We show that every two-player stochastic game with finite state and action sets and bounded, Borel-measurable, and shift-invariant payoffs, admits an $\ep$-equilibrium for all $\varepsilon>0$.
The theory of mean field games is a tool to understand noncooperative dynamic stochastic games with a large number of players. Much of the theory has evolved under conditions ensuring uniqueness of the mean field game Nash equilibrium.…
We formulate and study a two-player static duel game as a nonzero-sum discounted stochastic game. Players $P_{1},P_{2}$ are standing in place and, in each turn, one or both may shoot at the other player. If $P_{n}$ shoots at $P_{m}$ ($m\neq…
Nash equilibrium is used as a model to explain the observed behavior of players in strategic settings. For example, in many empirical applications we observe player behavior, and the problem is to determine if there exist payoffs for the…
In this work we study of competitive situations among users of a set of global resources. More precisely we study the effect of cost policies used by these resources in the convergence time to a pure Nash equilibrium. The work is divided in…
We introduce a novel class of Nash equilibrium seeking dynamics for non-cooperative games with a finite number of players, where the convergence to the Nash equilibrium is bounded by a KL function with a settling time that can be upper…
In this paper, we introduce the concept of infinitely split Nash equilibrium in repeated games in which the profile sets are chain-complete posets. Then by using a fixed point theorem on posets in [8], we prove an existence theorem. As an…
We study $n$-dimensional contests between two players with heterogeneous effort costs, where each dimension (battle) is modeled as a Tullock contest. Prize-allocation rules are identity-independent, budget-balanced, and weakly increasing in…
This paper is devoted to Nash equilibrium for games in capacities. Such games with payoff expressed by Choquet integral were considered by Kozhan and Zarichnyi (Nash equilibria for games in capacities, Econ. Theory {\bf 35} (2008) 321--331)…
We show that the problem of finding an {\epsilon}-approximate Nash equilibrium in an anonymous game with seven pure strategies is complete in PPAD, when the approximation parameter {\epsilon} is exponentially small in the number of players.
While it is known that shared quantum entanglement can offer improved solutions to a number of purely cooperative tasks for groups of remote agents, controversy remains regarding the legitimacy of quantum games in a competitive setting--in…
We consider a general nonzero-sum impulse game with two players. The main mathematical contribution of the paper is a verification theorem which provides, under some regularity conditions, a suitable system of quasi-variational inequalities…
We consider graphical $n$-person games with perfect information that have no Nash equilibria in pure stationary strategies. Solving these games in mixed strategies, we introduce probabilistic distributions in all non-terminal positions. The…
We propose a general class of symmetric games called position-optimization games. Given a probability distribution $Q$ over a set of targets $\mathcal{Y}$, the $n$ players each choose a position in a space $\mathcal{X}$. A player's utility…
We study the deterministic and randomized query complexity of finding approximate equilibria in bimatrix games. We show that the deterministic query complexity of finding an $\epsilon$-Nash equilibrium when $\epsilon < \frac{1}{2}$ is…
We consider a variant of Cournot competition, where multiple firms allocate the same amount of resource across multiple markets. We prove that the game has a unique pure-strategy Nash equilibrium (NE), which is symmetric and is…
We consider a nonzero-sum Markov game on an abstract measurable state space with compact metric action spaces. The goal of each player is to maximize his respective discounted payoff function under the condition that some constraints on a…
In a multi-objective game, each individual's payoff is a \emph{vector-valued} function of everyone's actions. Under such vectorial payoffs, Pareto-efficiency is used to formulate each individual's best-response condition, inducing…
We investigate the problem of equilibrium computation for "large" $n$-player games. Large games have a Lipschitz-type property that no single player's utility is greatly affected by any other individual player's actions. In this paper, we…
A multi-player competitive Dynkin stopping game is constructed. Each player can either exit the game for a fixed payoff, determined a priori, or stay and receive an adjusted payoff depending on the decision of other players. The single…