International Game Theory Review

A class of linear pursuit-evasion games with first-order acceleration dynamics and bounded controls is considered, where the evader has perfect information and the pursuer has delayed information on the lateral acceleration of the evader. The other state variables are perfectly known to the pursuer. This game can be transformed to a perfect information delayed control game with a single state variable, the centre of the uncertainty domain created by the information delay. The delayed dynamics of the game is transformed to a linear first-order partial differential equation coupled with an integral-differential equation, both without delay. These equations are approximated by a set of K + 1 ordinary differential equations of first order, creating an auxiliary game. The necessary conditions of optimality derived for the auxiliary game lead to the solution of the delayed control game by a limit process as K → + ∞. The solution has the same structure as the other, already solved, perfect information linear pursuit-evasion games with bounded controls and indicates that the value of the delayed information pursuit-evasion game is never zero. Asymptotic expressions of the value of the game for small and large values of the information delay are derived.

This paper provides general conditions on the direct demand functions in a Bertrand duopoly with differentiated substitute products and constant marginal costs, that allow an unambiguous ranking of firms' equilibrium payoffs between sequential play (with both order of moves) on the one hand, and simultaneous play on the other. The main results are that (i) when prices are strategic complements, both firms prefer sequential moves (with either order) to simultaneous moves, (ii) when prices are strategic substitutes, both firms prefer simultaneous moves to moving second in sequential play, and (iii) in the mixed strategic substitute/complement case, one firm is as in (i) and the other as in (ii). Thus, sequential moves would plausibly endogenously emerge in cases (i) and (iii), with one specified leader in the latter case. The analysis relies crucially on the theory of supermodular games, and is conducted at a high level of generality, dispensing with concavity-type assumptions, and taking into account both the issues of existence and possible non-uniqueness of the different equilibria involved.

One form of bounded rationality is a breakdown in the commonality of the knowledge that the players are rational. In Rubinstein's two-person alternating-offer bargaining game, assuming time preferences with constant discount factors, common knowledge of rationality is necessary for an agreement on a subgame perfect equilibrium (SPE) partition to be reached (if ever). In this note, assuming time preferences with constant costs of delay, we show that common knowledge of rationality is not necessary to reach always an agreement on a SPE partition. This result is robust to a generalisation, time preferences with constant discount factors and costs of delay, if the players are sufficiently patient.

The paper presents a method of supporting certain solutions of two-person bargaining games by unique Nash equilibria of associated games in strategic form. Among the supported solutions is the Kalai-Smorodinsky solution.

The paper is devoted to the problem of the equivalence of the strategies in extensive form games. The notion of H-strategies is introduced and it is proved that every strategy is equivalent to a certain H-strategy.

In congestion games, players use facilities from a common pool. The benefit that a player derives from using a facility depends, possibly among other things, on the number of users of this facility. The paper gives an easy alternative proof of the isomorphism between exact potential games and the set of congestion games introduced by Rosenthal (1973). It clarifies the relations between existing models on congestion games, and studies a class of congestion games where the sets of Nash equilibria, strong Nash equilibria and potential-maximising strategies coincide. Particular emphasis is on the computation of potential-maximising strategies.

The paper studies the consequences of the Null Player Out (NPO) property for single-valued solutions on the class of cooperative games in characteristic function form. We allow for variable player populations (supports or carriers). A solution satisfies the NPO property, if elimination of a null player does not affect the payoffs of the other players. Our main emphasis lies on individual values. For linear values satisfying the null player property and a weak symmetry property, necessary and sufficient conditions for the NPO property are derived.