N-person Non-cooperative Game Research Articles

Non-cooperative n-person game with a stopped set

A continuous time non-cooperative n-person Markov game with a stopped set is studied in this paper. We prove that, in the game process with or without discount factor, there exists an optimal stationary point of strategies, called the equilibrium point, and each player has his equilibrium stationary strategy, such that the total expected discounted or non-discounted gain are maximums.

Incomplete Information in Differential Games and Team Problems: Necessary and Sufficient Optimality Conditions

We study a non-classical structure of incomplete information in N-person non-cooperative differential games, team problems and stochastic control, where the noisy observations available to the decision makers are instantaneous and memoryless. Necessary and sufficient optimality conditions are obtained by a dynamic programming method, giving a characterization of the "signaling effect" and a separation principle

Nash Equilibria for Noncooperative n-Person Games in Normal Form

This paper concentrates on the problem of the existence of $\varepsilon $-equilibrium points in the Nash sense for noncooperative n-person games in normal form. Firstly, a survey of known $\varepsilon $-equilibrium.point theorems and proof techniques is given. Then various new $\varepsilon $-equilibrium point theorems are derived, in which one of the players has a big strategy space and where nonbounded, payoff functions are allowed. To prove these theorems, results of Arzela–Ascoli are extended.

Stable Situations in Non-Cooperative Games

The paper suggests on approach to solution of a class of n-person non-cooperative multi-step games with a finite after-effect and shows it’s application to solving industrial management problems. Based on the approach an algorithm for finding stable points was developed.

Viability, preference, and coalitions in the french election of 1951

Elections as a social choice institution have, of course, received intensive theoretical consideration in Public Choice. However, attention has largely been focused on situations that can be represented as n-person noncooperative games among candidates or parties, with particular emphasis on two-person constant-sum games. While mathematical facility has had much to do with these theoretical developments, the prevalence of the two-party system in the United States perhaps has also had an influence. Yet multiparty systems are in presence in much of the world. Multicandidate primaries already common in the U.S. have been further encouraged by recent proposals for proportional representation in Presidential primaries. The voter in a multicandidate or multiparty race is faced with a complex decision task. Viability as well as preference must be taken into account (McKelvey and Ordeshook, 1972; Kramer, 1968). Thus the voter may rationally vote for a candidate other than that candidate whose "position" is "closest" to the voter's.1 Moreover, in addition to considering the impact of his vote on eventual governing

On a formulation of discrete, N-person non-cooperative games

We present a method of formulatingn-person non-cooperative games and a means of finding their equilibrium points.

On Behavior Strategy Solutions in Two-Person Zero-Sum Finite Extended Games with Imperfect Information. Part I: A Method for Determination of Minimally Complex Behavior Strategy Solutions

In any two-person zero-sum finite extended game with imperfect information, an upper bound on the quality of each player’s strategies is established by his choice of a scheme for gathering and retaining the information that becomes available to him as the game progresses. Further, for a given game, strategies of the maximum possible quality may exist for each player on a number of information schemes of widely differing complexities.By analyzing the relationship between any given two-person zero-sum finite extended game with given information schemes for its players, and an associated N-person noncooperative game, a heuristic scheme is uncovered for searching for minimally complex information schemes which support behavior strategies having within $\varepsilon $ of the maximum possible quality, for any given $\varepsilon $.In the course of this analysis, a minimax theorem in behavior strategies is obtained, which is similar to von Neumann’s minimax theorem in mixed strategies.

Noncooperative N-person game theory (N≥2) using expected relative desirability criterion

Considered is noncooperative discrete N-person game theory forN≥2 (where the players choose their strategies separately and independently). Payoffs can be of a very general nature and are not necessarily numbers. However, each player is able to quantitatively specify the relative desirability of the possible game outcomes (N-dimensional, a pay off to each player) according to his preferences. That is, he specifies a positive number for each outcome and these numbers are such that their ratios quantitatively represent the relatively desirability of the corresponding outcomes to this player. For each player, the criterion is the expected relative desirability to him of what occurs for the game, and an optimum mixed strategy maximizes the minimum value of this criterion over all possible mixed strategies that could be used by the other players. An optimum solution is obtained by used of classical minimax game theory. Practical implications of applying thisN-person game theory are examined. Also, a possible approach for developing quantitative functions to provide the relative desirability numbers is outlined.

Probability of a pure equilibrium point in n-person games

A “random” n-person non-cooperative game—the game that prohibits communication and therefore coalitions among the n players—is shown to have with high probability a pure strategy solution. Such a solution is by definition an equilibrium point or a set of strategies, one for each player, such that if n−1 players use their equilibrium strategies then the n-th player has no reason to deviate from his equilibrium strategy. It is shown that the probability of a solution in pure strategies for large random n-person games converges to (1−1/ e) for all n≥2.