International Game Theory Review

This paper analyzes coordination in tacit collusion when firms’ discount factor is private information. We consider an infinitely repeated duopoly where two states of the world randomly occur, with different incentives for collusion. Depending on its own discount factor, a firm chooses cooperative behavior in both states (patient), in none of the states (impatient) or in one state (mildly patient). The presence of different states affects the strategic role of beliefs. A mildly patient firm has an incentive in “faking patience” to get the deviation profit. Interestingly, this effect prevents or delays collusion when the belief in patience is strong.

In this paper, we build and investigate cooperative games with different characteristic functions (von Neumann–Morgenstern, Petrosyan–Zaccour, Gromova–Petrosyan) on the base of symmetrical Cournot oligopoly game-theoretic models in normal form. We find Nash and Stackelberg equilibria and cooperative solutions for nonsymmetrical Cournot oligopoly game-theoretic models in normal form. Also, we build and investigate cooperative three-player games with the same characteristic functions on the base of these models, including the calculation of Shapley value. We compare payoffs received by the players according to different optimality principles of cooperative games and games in normal form.

In this paper, we explore network situations where the architecture of the network is described by a hypergraph. In a hypergraph, nodes are the players and — in contrast to bilateral graphs — links between players may involve more than just two players. The value function is defined on the architecture of the network such that different hypergraphs that connect the same individuals can generate different values. We provide axiomatic characterizations for the Myerson value and the position value. Furthermore, we define the notion of the core of a hypergraph situation. By means of an example, we also show that the Myerson value and the position value can lie in the core of a hypergraph situation.

This paper establishes an analytical framework for cooperative public choice games. In a cooperative public choice game under unanimity rule, all the players who belong to the only coalition will equally divide the cooperative payoff surplus, the equilibrium public choice is the one which can bring about the maximum cooperative payoff among all the public choices. In a cooperative public choice game under majority rule, compared with other public choices, the public choice with maximum comparative payoff will finally win the required majority of votes because of its greatest capability of attracting the intermediate team. When in a public choice game under majority rule there are more than two public choices which can bring about the maximum comparative payoff to the supporter coalition, the equilibrium choice will be the same one in the same public choice game under unanimity rule.

This paper studies extensions of the core and the equal split off set (ESOS) for TU games, and also subsolutions of the extensions in order to derive some new egalitarian solutions for TU games. Stability of the allocations is weakened such that an allocation $x$ can be blocked only by rich coalitions which together with a player will contain all players having payoffs not less than him. In accordance with such a definition of blocking, two new solutions — the rich core and the egalitarian rich core — are defined and characterized by means of weakening of axioms characterizing the ESOS on the class of all TU games [Dietzenbacher, B. and Yanovskaya, E. [2021] Consistency of the equal spit-off set, Int. J. Game Theory 50(1), 1–22]. Two subsolutions of the egalitarian rich core — the set of Lorenz undominated allocations and the set of allocations that lexicographically minimize maximal payoffs of players (Lmax solution) are characterized. The tight upper boundary of the number of allocations in the ESOS and in the egalitarian rich core is found.

A differential game described by a nonlinear system of differential equations is considered in a finite-dimensional Euclidean space. The value set of the pursuer control is a finite set. The value set of the evader control is a compact set. The purpose of the pursuer is a translation of the system in a finite time to any given neighborhood of zero. The pursuer uses a piecewise open-loop strategy constructed only by using information on the state coordinates and the velocity in the partition points of a time interval. In the past work, sufficient conditions were obtained for existence of a neighborhood of zero from which the capture occurs. The statement of the capture theorem contains such a condition that some vectors set up a positive basis. In this research, we consider the case when these vectors set up a one-sided set. For this case, sufficient conditions are obtained for existence of a set of initial position, from which the capture occurs.