International Game Theory Review

We prove a new theorem for the existence of equilibrium in discontinuous games in which the players’ preferences are neither complete nor transitive. Our result is an alternative version of Shafer and Sonnenschein ([1975] J. Math. Econ. 2, 345–348), He and Yannelis ([2016] Econ. Theory 61, 497–513), Reny ([2016] Econ. Theory Bull.) and Carmona and Prodczeck ([2016] Econ. Theory 61, 457–478).

This paper takes an axiomatic approach to the revenue sharing problem for an airline alliance network. We propose a simple sharing rule that allocates the revenue of each flight equally among the carriers of the flight. We show that it is the only rule satisfying the axioms of separability, the null airline property and equal treatment of equals. We show that the rule coincides with the Shapley value of the game associated with the problem. We provide two extensions of the rule, allowing it to depend on the lengths or the capacities of the flight legs. We also consider the maximum revenue problem for the airline alliance. We propose a simple integer linear programming model. We examine its Owen set. Lastly, we provide an algorithm to compute both the optimal solution and the revenue sharing solution given by the simple sharing rule for the maximum revenue problem.

In two-sided matching markets where direct negotiations take place over the division of profits between the partners, the appropriate solution concept is the core. Only a minority of the experimentally observed bargaining results are within the core, and the number of core solutions further decreases with an increase in market complexity. For differently-sized matching markets, two adjustments to the core requirements are introduced. Projected cores from smaller markets (partial condition core) are confirmed in larger markets. The possibility of Pareto improvements from the perspective of individual players (individual condition core) does not vanish but may even increase with market size. In all the investigated experimental markets, a high percentage of equal profit splits between matching partners in face-to-face bargaining was found, especially in larger, decentralized matching markets.

This paper handles the problem of intercepting a superior missile using a formation of lower-capabilities pursuers. The problem is formulated as multi-player differential game and solved using optimal control techniques. This approach makes use of the Apollonius circles as a final path constraint of the problem in order to achieve the capturing conditions. Additionally, a dimensionality reduction technique based on differential flatness property of the formation is investigated.

We analyze the effect of customizing a product on the ability of firms to tacitly collude on prices. Following [Bar-Isaac et al. [2014] Targeted product design: Locating inside the Salop circle, Mimeo], we allow firms to be located inside the circle in the Salop model [Salop, S. [1979] Monopolistic competition with outside goods, Bell J. Econ., 10(1), 141–156]. Our analysis shows that the effect of product customization on the stability of collusion depends on the sensitivity of consumers’ utility to the degree of customization. In particular, if that sensitivity is low enough, then greater customization facilitates collusion. Otherwise, greater customization hinders collusion if consumers value the product little.

It is a classical and interesting problem to find a Nash equilibrium of noncooperative games in the strategic form. It is well known that the game always has a mixed-strategy Nash equilibrium, but it does not necessarily have a pure-strategy Nash equilibrium. Takeshita and Kawasaki proved that every noncooperative partially monotone game has a pure-strategy Nash equilibrium, that is, the partial monotonicity is a sufficient condition for a noncooperative game to have a pure-strategy Nash equilibrium. In this paper, we prove the necessary and sufficient condition for a noncooperative $n$-person game with $n\ge 2$ to be partially monotone. This result is an improvement of Takeshita and Kawasaki’s result.