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Considered here are equilibria, notably those that solve noncooperative games. Focus is on connections between evolutionary stability, concavity and monotonicity. It is shown that evolutionary stable points are local attractors under gradient dynamics. Such dynamics, while reflecting search for individual improvement, can incorporate myopia, imperfect knowledge and bounded rationality/competence.

Nash equilibrium leaves the impression that each player foresees perfectly and responds optimally. Must human-like, rational agents really acquire both these faculties? This paper argues that in some instances neither is ever needed. For the argument repeated play is modelled here as a constrained, decentralized, second-order process driven by noncoordinated pursuit of better payoffs. Some friction feeds into — and stabilizes — a fairly myopic mode of behavior. Convergence to equilibrium therefore obtains under weak and natural conditions. An important condition is that accumulation of marginal payoffs, along the path of play, yields a sum which is bounded above.

This paper considers a fairly large class of noncooperative games in which strategies are jointly constrained. When what is called the Ky Fan or Nikaidô-Isoda function is convex-concave, selected Nash equilibria correspond to diagonal saddle points of that function. This feature is exploited to design computational algorithms for finding such equilibria.

To comply with some freedom of individual choice the algorithms developed here are fairly decentralized. However, since coupling constraints must be enforced, repeated coordination is needed while underway towards equilibrium.

Particular instances include zero-sum, two-person games — or minimax problems — that are convex-concave and involve convex coupling constraints.

In this paper we consider a special class of n-person potential games and investigate partial cooperation between a portion of the players that sign a cooperative agreement. Existence results of partial cooperative equilibria are obtained and some possible applications are discussed, particularly a Cournot oligopoly and an international water resources management model.

In this paper we study and compute E-points in an explicit way for a special kind of diagonal games with 3k + 1, 4k + 3 and sk + 1 players where 1 ≤ s ≤ k.

We consider an extension of strategic normal form games with a phase before the actual play of the game, where players can make binding offers for transfer of utilities to other players after the play of the game, contingent on the recipient playing the strategy indicated in the offer. Such offers transform the payoff matrix of the original game but preserve its noncooperative nature. The type of offers we focus on here are conditional on a suggested matching offer of the same kind made in return by the receiver. Players can exchange a series of such offers, thus engaging in a bargaining process before a strategic normal form game is played. In this paper, we study and analyze solution concepts for two-player normal form games with such preplay negotiation phase, under several assumptions for the bargaining power of the players, as well as the value of time for the players in such negotiations. We obtain results describing the possible solutions of such bargaining games and analyze the degrees of efficiency and fairness that can be achieved in such negotiation process. We show the similarities and the differences with a variety of frameworks in the literature of bargaining games and games with a preplay phase.

Game theory-based models are widely used to solve multiple competitive problems such as oligopolistic competitions, marketing of new products, promotion of existing products competitions, and election presage. The payoffs of these competitive models have been conventionally considered as deterministic. However, these payoffs have ambiguity due to the uncertainty in the data sets. Interval analysis-based approaches are found to be efficient to tackle such uncertainty in data sets. In these approaches, the payoffs of the game model lie in some closed interval, which are estimated by previous information. The present paper considers a multiple player game model in which payoffs are uncertain and varies in a closed intervals. The necessary and sufficient conditions are explained to discuss the existence of Nash equilibrium point of such game models. Moreover, Nash equilibrium point of the model is obtained by solving a crisp bi-linear optimization problem. The developed methodology is further applied for obtaining the possible optimal strategy to win the parliament election presage problem.

We consider the problem of approximating Nash equilibria of $N$ functions $f_1,\dots ,f_N$ of $N$ variables. In particular, we show systems of the form