International Game Theory Review

Nash’s [1953] demand game models the second step in a “two-move game” that formalizes his “Negotiation Model”. Nash claimed for any two-person bargaining game $(S,d)$ the existence of a unique stable equilibrium of its associated second move demand game that by its payoff vector supports the symmetric Nash solution of that bargaining game.

Nash’s negotiation game is considered the first contribution to the Nash program. Only weaker versions of stability than that claimed by Nash have been formally proven later by other authors. However, Nash’s request for “studying the relative stabilities” of the demand game’s equilibria has never been complied with. By performing that task, we establish analogous stability results for all generalized Nash solutions and thereby disprove Nash’s “unique stability” claim.

Furthermore, we explain the impact of our result on the Nash solution with endogenous variable threats (NBWT) of the two move negotiation game, which is defined as the symmetric Nash solution of that bargaining game $(S,d^{\ast })$ whose status quo point $d^{\ast }$ is the unique payoff vector of the payoff-equivalent equilibria of the first move threat game.

This study develops a model to explain why accounting procedures, also known as Generally Accepted Accounting Principles, are “generally accepted”. For this purpose, we focus on depreciation defined as the rational and systematic allocation of the original cost of an asset over the expected useful life of that asset. We investigate what it means to be “rational” using cooperative game theory. We show that cost allocations determined by the straight-line (SL) method, which is conventionally used worldwide, are elements of the core and that the conditions of the core can be rational in practice. Furthermore, we examine the relationship between the SL method and other solution concepts, such as the Shapley value and the nucleolus. Our next step is to clarify the characteristics besides the core selection of the SL method, those of other depreciation methods used in practice, and the logical relations between these characteristics.

We give two generalizations of the Zhou fixed point theorem. They weaken the subcompleteness condition of values, and relax the ascending condition of the correspondence. As an application, we derive a generalization of Topkis’ theorem on the existence and order structure of the set of Nash equilibria of supermodular games.

In this paper, we provide a novel approach to achieving a desired outcome in a coordination game: the original $2\times 2$ game is embedded in a $2\times 3$ game where one of the players may use a third action. For a large set of payoff values, only one of the Nash equilibria of the original $2\times 2$ game is stable under replicator dynamics. We show that this Nash equilibrium attracts all initial conditions in the interior of the state space for the modified $2\times 3$ game. Thus, the existence of a third action for one of the players, although not used, allows both players to coordinate on one Nash equilibrium.

This Nash equilibrium is the one preferred by, at least, the player with access to the new action. This approach deals with both coordination failure (players choose the payoff-dominant Nash equilibrium, if such a Nash equilibrium exists) and miscoordination (players do not use mixed strategies).

This paper introduces information asymmetry, cooperation and payoff compensation mechanism into public choice games, and establishes an analytical frame for information asymmetric cooperative public choice games. This paper examines the coalition formation and the distribution of the cooperative payoff under the equilibrium public choice (if it does exist) in an information asymmetric public choice game under unanimity rule and those in an information asymmetric public choice game under majority rule, respectively. Arrow [1951] and Sen [1970] assumed that there is no cooperation and payoff compensation mechanism in a public choice game, and showed that rational individuals with individual sovereignty could not reach consensus on any public choice. This paper shows that, even in a public choice game of information asymmetry, the cooperation and payoff compensation mechanism may lead to the coalition equilibrium, the achievement of equilibrium public choice, and the distribution equilibrium of cooperative payoff of the coalition which supports the equilibrium public choice, whether the public choice games are under unanimity rule or under majority rule.

This study examines an environmental management strategy to effectively cap greenhouse gas (GHG) emissions in an electricity market. To do so, we model a stochastic impulse two-person, nonzero-sum game between a power plant, a representative of electricity production within a country whose primary aim is to maximize profits, and government who is motivated to minimize the social and environmental cost of pollution. We assume that the power plant’s competitive price is equal to the marginal cost whilst the government’s running cost is linear. When the uncontrolled output of GHG emissions evolves as a Geometric Brownian motion, we provide a more dynamic and robust depiction of the interplay between government and the energy sector. We provide solutions to the impulse control problem derived via the quasi-variational inequalities (QVIs). We then present a sufficiency criterion for the existence of a Nash equilibrium for the optimal policy. Ultimately, our use of short-run price competition characterized by strategic supplies for renewable and fossil resources and inclusion of endogenous constraints on production capacity provides a more robust model and an effective framework for the development of policy that allows governments to meet emissions targets whilst guaranteeing energy supply.