International Game Theory Review

A pursuit–evasion differential game of prescribed duration with bounded controls is considered. The evader has two possible dynamics, while the pursuer dynamics is fixed. The evader can change its dynamics once during the game and its initial lateral acceleration is nonzero. The pursuer knows the possible dynamics of the evader, but not the actual one. Due to the different information sets of the players the game is not zero-sum. The robust capture zone of the pursuer and the robust escape zone of the evader are constructed and analyzed. Since the game is not zero-sum the robust capture/escape zones do not complement each other. Illustrative examples are presented.

This paper presents a new systematic review of N-person social dilemma games using a new approach based on dynamic properties of the corresponding system. Traditionally N-person social dilemma games are classified by relative orders of magnitude of payoff parameters. Without border-line cases 24 are identified. The new approach introduced in this paper categorizes the social dilemma games in cases with different number and asymptotic properties of the equilibria. In these cases the solution structure or the trajectory of the percentage of cooperators is readily apparent. These cases also provide the modeler with additional information concerning the impacts of the model parameters on the game outcomes. The example of a simple cartel illustrates this methodology.

Carbon leakage and competitiveness concerns are some of the main reasons why an international environmental agreement is lacking to fight climate change. Many studies discussed the adoption of a border tax adjustment (BTA) to allow countries that would like to implement a carbon tax to level the playing field with imports. The big drawback from these studies is that the other country is not allowed to react by adopting itself a carbon tax to avoid being punished with the BTA. The model proposed in this paper looks at the optimization of two different governments and their respective firms. Parametric values inside the set [0, 1) are used to represent the possible extents of the BTA depending on both countries environmental policy allowing countries to have different carbon policies. The result that a BTA parameter of 0.5 yields the highest total welfare could increase its acceptance within the World Trade Organization (WTO).

In the paper two-person nonzero-sum semi-infinite games with bounded payoffs are studied — both with countable and uncountable infinite strategy space. Under some concavity/convexity assumptions they are shown to possess ε-equilibria (equilibria) in strategies with supports consisting of at most two points of the players' pure strategy spaces. Further the games without any concavity/convexity properties are studied. It is proved that they possess ε-equilibria (equilibria) in strategies having certain finite supports.

In this paper we introduce two related core-type solutions for games with transferable utility (TU-games) the -core and the -core. The elements of the solutions are pairs where x, as usual, is a vector representing a distribution of utility and is a balanced family of coalitions, in the case of the -core, and a minimal balanced one, in the case of the -core, describing a plausible organization of the players to achieve the vector x. Both solutions extend the notion of classical core but, unlike it, they are always nonempty for any TU-game. For the -core, which also exhibits a certain kind of "minimality" property, we provide a nice axiomatic characterization in terms of the four axioms nonemptiness (NE), individual rationality (IR), superadditivity (SUPA) and a weak reduced game property (WRGP) (with appropriate modifications to adapt them to the new framework) used to characterize the classical core. However, an additional axiom, the axiom of equal opportunity is required. It roughly states that if belongs to the -core then, any other admissible element of the form should belong to the solution too.

We compare the seller's expected revenue in asymmetric second-price auctions with the benchmark case where all bidders have the average distribution. We show that with two bidders, asymmetry has a negative effect on revenue. However, for n > 2 bidders there is no clear observation we can make. We prove that in the case of weak asymmetry, sellers prefer asymmetry over low valuations and symmetry over high valuations. In addition, we show that a good approximation for the expected revenue in the case of weak asymmetry can be obtained by calculating the revenue of the symmetric auction with identical distributions equal to the geometric or arithmetic average.