International Game Theory Review

Social pressures, in addition to the law, incite more and more firms to pursue multiple and separate objectives. This trend raises the following question: will the change in the number of objectives pursued by firms affect their strategic interactions? To address this issue we focus on a dynamic duopoly where each firm has two objectives: one of the firms’ objectives is financial and the other is environmental. Production is a polluting activity and the actual level of pollution depends on current and past emissions. We analyze both open-loop Nash and cooperative equilibria (these equilibria are also trivially feedback as the equilibrium strategies are constant). We show that contrary to the case where firms’ unique objective is the financial one, there are Nash equilibria where production is lower than in the cooperative equilibrium. This stems from the fact that in a Nash equilibrium firms do not coordinate the choice of the relative weight given to the environmental objective. We obtain the same conclusion when firms can mitigate pollution. In this case, we also show that there are Nash equilibria where the sum of the firms’ mitigation efforts is higher than its value in the cooperative equilibrium.

In this paper, we consider a pollution control problem along a river basin where a portion of the pollution emitted by the upstream region can be transferred to the downstream region. Our model has three significant features: first, we take into account the pollution abatement investment, and the stock of pollution abatement capital follows standard differential equation of motion; second, we introduce the emission permits trading system so that each region has the choice between buying pollution permits or pollution abatement investment; third, we consider the pollution compensation mechanism so that the downstream region pays pollution compensation for the upstream region. We explore and compare the optimal decisions of both the upstream and downstream regions under the cases of the cooperative and no-cooperative strategies, respectively. We find that although the flow of emissions can be better controlled by cooperation between the upstream and downstream regions, the pollution abatement investment is not necessarily higher in the cooperative equilibrium. Further, a sensitivity analysis is also conducted on the parameters of the transboundary river basin pollution.

In this paper, we introduce minimum cost spanning tree problems with multiple sources. This new setting is an extension of the classical model where there is a single source. We extend several definitions of the folk rule, the most prominent rule in the classical model, to this new context: first as the Shapley value of the irreducible game; second as an obligation rule; third as a partition rule and finally through a cone-wise decomposition. We prove that all the definitions provide the same cost allocation and present two axiomatic characterizations.

Two structured classes of zero-sum two-person finite (state and action spaces) semi-Markov games with discounted payoffs, namely, Additive Reward-Additive Transition and Action Independent Transition Time (AR-AT-AITT) and Additive Reward-Action Independent Transition and Additive Transition Time (AR-AIT-ATT) have been studied. We propose two practical situations of economic competition viz. petroleum game and groundwater game that suitably fit into such classes of games, respectively. Solution (value and pure stationary optimals) to such classes of games can be derived from optimal solution to appropriate bilinear programs with linear constraints. We present a stepwise generalized principal pivoting algorithm for solving the vertical linear complementarity problem (VLCP) obtained from such game problems. Moreover, a neural network dynamics is proposed for solving such structured classes. Examples are worked out to compare the usefulness of the above three algorithms.

Not only in control problems, but also in dynamic games, several sources of performance degradation, such as model variation, deterministic and stochastic uncertainties and state delays, need to be considered. In this paper, we present an $H_{\infty }$ constrained Pareto suboptimal strategy for stochastic linear parameter-varying (LPV) time-delay systems involving multiple decision makers. The goal of developing the $H_{\infty }$ constrained Pareto suboptimal strategy set is to construct a memoryless state feedback strategy set, so that the closed-loop stochastic LPV system is stochastically mean-square stable. In the paper, the existence condition of the extended bounded real lemma is first established via linear matrix inequalities (LMIs). Then, a quadratic cost bound for cost performance is derived. Based on these preliminary results, sufficient conditions for the existence of such a strategy set under the $H_{\infty }$ constraint are derived by using cross-coupled bilinear matrix inequalities (BMIs). To determine the strategy set, a viscosity iterative scheme based on the LMIs is established to avoid the processing of BMIs. Finally, two numerical examples are presented to demonstrate the reliability and usefulness of the proposed method.

The overexploitation of common pool resources is frequently associated with open access regimes in which each resource user operates independently of all other resource users. The outcome is a Nash equilibrium of the prisoner’s dilemma. Restricted access regimes of the sort identified by Ostrom and colleagues typically ensure that individual resource users do not operate independently. Taking a quantum approach to the theory of games, we argue that the institutional arrangements involved in common pool resource management imply the “entanglement” of the strategies of resource users. For a very simple case — two firms exploiting a common pool fishery — we show that there exists an “entanglement” mechanism that assures the cooperative outcome.