International Game Theory Review

In this paper reasonable payoff intervals for players in a game in partition function form (p.f.f. game) are introduced and used to define the notion of compromisable p.f.f. game. For a compromisable p.f.f. game a compromise value is defined for which an axiomatic characterization is provided. Also a generic subclass of games in extensive form of perfect information without chance moves is introduced. For this class of perfect extensive form games there is a natural credible way to define a p.f.f. game if the players consider cooperation. It turns out that the p.f.f. games obtained in this way are compromisable.

We consider a game-theoretic model of counterproliferation, in which a single Incumbent (holding nuclear weapons) is faced with a sequence of potential Entrants (who are considering developing and deploying a nuclear capability or other weapons of mass destruction of their own). The Incumbent can either choose to act preemptively, with certain costs, or allow the Entrants to deploy a nuclear capability, with consequent costs due to the potential for nuclear blackmail. How should each of the players decide?

The players' decisions are optimally based not only on their own cost functions (which each knows) but also on their opponent's cost structure (which is known only in probability). Entrants (other than the first) can learn something about the Incumbent's cost structure from decisions they have made in the past. It turns out that, depending on a would-be Entrant's cost structure, a record of preemption by the Incumbent can have either a deterrent or provocation effect. Understanding the basis for each of these contradictory effects is critical to designing an optimal counterproliferation strategy.

It has been recently proved that the non-existence of certain type of cycles of pre-imputation, fundamental cycles, is equivalent to the balancedness of a TU-games (Cesco (2003)). In some cases, the class of fundamental cycles can be narrowed and still obtain a characterization theorem. In this paper we prove that existence of maximal U-cycles, which are related to a transfer scheme designed for computing a point in the core of a game, is condition necessary and sufficient for a TU-game be non-balanced, provided n - 1 and n-person are the only coalitions with non-zero value. These games are strongly related to games with only 1, n - 1 and n-person permissible coalitions (Maschler (1963)).

This paper studies a transboundary pollution problem between two neighbour regions as a dynamic game. These two regions do not only share an environmental problem but they are also engaged in interregional trade. A good produced in one region is traded to the other which uses it as an input. This intermediate good is supplied by the former and demanded by the latter. The supply-demand scheme determines the price and production of the intermediate good. Thus total production is fixed in both regions, and the emissions of pollutants are also determined as a by-product. Cooperation cuts down production and trade, and in consequence the emissions of pollutants. Therefore, the environmental gain from cooperation overcomes the shrink in the interregional trade. An allocation mechanism to share the surplus of cooperation is defined, which guarantees a time-consistent agreement between both regions.

This paper investigates a class of dynamic selection processes for n-person normal-form games which includes the Brown-von Neumann-Nash dynamics. For (two-person) zero-sum games and for (n-person) potential games every limit set of these dynamics is a subset of the set of Nash-equilibria. Furthermore, under these dynamics the unique Nash-component of a zero-sum game is minimal asymptotically stable and for a potential game a smoothly connected component which is a local maximizer is minimal asymptotically stable.

This paper shows how strategic matching generates reputation-building behavior in an evolutionary chain-store game. Strategic matching means the possibility for an entrant to choose in a strategic way the local market into which it will move. Players are boundedly rational and follow behavioral rules simply requiring that the frequency of any strategy enjoying the highest payoff should never decrease. In preventing the random entries in markets of "fighting monopolists", strategic matching reinforces the reputation effects. Using the bounded rationality set-up offered by evolutionary game theory, the paper follows Selten (1978)'s intuition underlying the necessity of a limited rationality approach in order to capture reputation effects.

We decompose the representative agent into her manager, worker and rentier selves. The criterion is the information set of each of the 'incarnations' at every stage of a repeated game. The rentier's information set includes anticipating information while the information set of the other agents is feedback. The equilibrium that results is, therefore, not subgame perfect. Enter the government that produces a good that complements the existing good. It is financed by the issue of money that substitutes for the asset. The enlargement of the state space of the game induces cooperation between the agents.

A computational procedure, Simulated Fictitious Play (SFP), is introduced to approximate equilibrium solutions for n-person, non-cooperative games with large strategy spaces. A variant of the iterative solution process fictitious play (FP), SFP is first demonstrated on several small n-person games with known solutions. In each case, SFP solutions are compared to those obtained through analytical methods. Sensitivity analyses are presented that examine the effects of iterations (repetitions of the stage game) and number of sample outcomes generated within each iteration on measures of convergence. The algorithm is then used to approximate the solution of a 20-player game, in which each player has 601 pure strategies. The resulting strategy space, 601²⁰, or 3.78 × 10⁵⁵, has proved virtually unmanageable for existing solution methods and computer software packages that employ numerical methods. The paper discusses the origins and theoretical development of FP, as well as interest in FP as a model of learning. It concludes with a discussion of both the potential and limitations of SFP.

I give necessary and sufficient conditions on the payoff set that guarantee uniqueness of the equilibrium in the Rubinstein bargaining model. The conditions encompass a class of non-convex or disconnected payoff sets with discontinuous Pareto frontiers. Roughly speaking, the equilibrium is unique if the objective function of the corresponding Nash-bargaining game has a unique maximum. I extend the analysis to games where the time between offers is not constant.

A formula is presented for computing the equilibrium payoffs in a generic finite two-person game when the support of the equilibrium is known.

In this paper, we study a non cooperative game with payoff functions involving fuzzy parameters. We introduce a concept of solution for this game that we call α-N-S- equilibrium. Our definition is derived from the concept of N-S equilibrium introduced by Zhukovskii for a non cooperative game with payoffs involving unknown parameters in the case of complete ignorance of their behavior. The α-N-S- equilibrium takes into account both the aspect of conflict and the aspect of decision making under uncertainty related to the presence of fuzzy parameters. For the aspect of conflict we adopted the Nash equilibrium, for the aspect of uncertainty we adopted the maximin approach through weak Pareto optimality. Furthermore, we give sufficient conditions for its existence.

When the strategy set of a game is a continuum, its discretization may not conserve local properties even for arbitrarily fine strategy grids. This paper provides two technical lemmata which are useful to deal with these problems in particular contexts. Four applications are presented, regarding the discretization of Cournot and Bertrand oligopolies, a consumer optimization problem, and an insurance market.

In this paper we introduce two simple versions of the hat game for three players and a generalization for n players. We compute the extensive version of the game and all the equilibrium and friendly equilibrium points as a simple example of the structure function.