Subgame Perfect Nash Equilibrium Outcome Research Articles

The Optimal Privatization Policies under an International Mixed Duopoly

This paper explores the socially optimal privatization policies under the setting of international mixed duopoly. We find that partial privatization is socially optimal under Cournot competition and private leadership competition, whereas full nationalization is socially optimal under public leadership competition. Moreover, the equilibrium social welfare under private leadership competition is higher than that observed under Cournot competition and that observed under private leadership competition, which differs from the findings of Matsumura (2003b). We also show that the endogenous timing game has a subgame perfect Nash equilibrium outcome, under which the government chooses a partial privatization policy, and private leadership competition emerges as the optimal output decision sequence of firms. An important policy implication from this paper is that the government should partially privatize the public firm and facilitate the emergence of private leadership competition in an international mixed market.

One-Seller Assignment Markets with Multi-Unit Demands

We consider one-seller assignment markets with multi-unit demands and prove that the associated game is buyers-submodular. Therefore the core is non-empty and it has a lattice structure which cont ains the allocation where every buyer receives his marginal contribution. We prove that in this kind of market, every pairwise-stable outcome is associated to a co mpetitive equilibrium and vice versa. We study conditions under which the buyers-optimal and the seller-optimal core allocations are competitive equilibrium payoff vectors. Moreover, we characterize the markets for which the core coincid ences with the set of competitive equilibria payoff vectors. When agents behave strategically, we introduce a procedure that implements the buyers-op timal core allocation as the unique subgame perfect Nash equilibrium outcome.

Endogenous timing in a mixed oligopoly with semipublic firms

An endogenous order of moves is analyzed in a mixed market where a firm jointly owned by the public sector and private domestic shareholders (a semipublic firm) competes with n private firms. We show that there is an equilibrium in which firms take production decisions simultaneously. This result is strikingly different from that obtained by Pal (Econ Lett 61:181–185, 1998), who shows that when a public firm competes with n private firms all firms producing simultaneously in the same period cannot be sustained as a Subgame Perfect Nash Equilibrium outcome. Our result differs from that of Pal (Econ Lett 61:181–185, 1998) for two reasons: firstly, we consider that there is a semipublic firm rather than a public firm. Secondly, Pal (Econ Lett 61:181–185, 1998) considers that the public firm is less efficient than private firms while in our paper all firms are equally efficient.

War and peace: Third-party intervention in conflict

This paper develops a simple sequential-move game to characterize the endogeneity of third-party intervention in conflict. We show how a third party's “intervention technology” interacts with the canonical “conflict technologies” of two rival parties in affecting the sub-game perfect Nash equilibrium outcome. From the perspective of deterrence strategy, we find that it is more costly for a third party to support an ally to deter a challenger from attacking (i.e., to maintain peace or acquiescence), as compared to the alternative case when the third party supports the ally to gain a disputed territory by attacking (i.e., to create war), ceteris paribus. However, an optimally intervening third party can be either “peace-making”, “peace-breaking”, or neither depending on the characteristics of the conflict and the stakes the third party holds with each of the rival parties.

Multilateral bargaining: conditional and unconditional offers

We present a game in which n persons split a cake, where a distinction between conditional and unconditional offers is made. This distinction sheds light on the contrasting results obtained in the previous literature of multilateral bargaining. By allowing the proposer to make both conditional and unconditional offers, we show that the game has a unique subgame perfect Nash equilibrium outcome.

Externalities and Renegotiations in Three-Player Coalitional Bargaining

This paper proposes a new solution concept to three-player coalitional bargaining problems. The coalitional bargaining problem is modeled as a dynamic non-cooperative game in which players make conditional or unconditional offers, coalitions continue to negotiate as long as there are gains from trade, and coalitions may create positive or negative externalities. The theory yields a unique stationary subgame perfect Nash equilibrium outcome - the coalitional bargaining value-that has an intuitive economic interpretation using endogenous outside options. Interestingly, this solution can either be the Nash bargaining solution, for games where the worth of all pairwise coalition is less than a third of the grand coalition value; the Shapley value, for games where the sum of the value created by all pairwise coalitions is greater than the grand coalition value; or the nucleolus, for games where only the 'natural coalition' among two 'natural partners' creates significant value, and those where only the two pairwise coalitions including a 'pivotal player' create significant value.

Mutual insurance and reputational collateral

A game between two infinitely lived economic agents is analysed. Each player is exposed to uncertainty with respect to individual endowments and maximises expected discounted utility. Contracts between agents are not enforceable. Players have no access to exogenous capital markets. Therefore they have incentives to provide some mutual insurance without contractual agreement. Autarky is always a subgame perfect Nash equilibrium outcome. Generically, with sufficiently high discount factors, there exists a subgame perfect trigger strategy equilibrium which both players prefer to autarky. When endowments are (perfectly) negatively correlated across players, full insurance plans can be implemented. When the individual endowment streams are Bernoulli processes and independent across players, partial insurance plans can be implemented.

Non-cooperative bargaining of N ⩾ 3 players

Abstract Extensions to N ⩾ 3 players of Rubenstein's (1982) bargaining model with fixed common discount factor are considered. If voting takes place simultaneously, then any partition of the cake is a subgame-perfect Nash equilibrium outcome.