Unilateral production restrictions in a dynamic duopoly

This paper examines a dynamic game of exploitation of a productive asset by a duopoly. A closed-loop Nash equilibrium of the game is constructed and used to analyze the effects of a unilateral production restriction. Surprisingly, such unilateral action may result in a decrease of the long-run asset's stock. We also exhibit production restrictions that can result simultaneously in an increase of the asset's stock and the long-run profits of the firm that is being imposed the production restriction. Moreover, a unilateral decrease of the production of one firm can induce its rival to also decrease its production.     

Strategic incentives in dynamic duopoly

We compare steady states of open loop and locally stable Markov perfect equilibria (MPE) in a general symmetric differential game duopoly model with costs of adjustment. Strategic incentives at the MPE depend on whether an increase in the state variable of a firm hurts or helps the rival and on whether at the MPE there is intertemporal strategic substitutability or complementarity. A full characterization is provided in the linear-quadratic case. Then with price competition and costly production adjustment, static strategic complementarity turns into intertemporal strategic substitutability and the MPE steady-state outcome is more competitive than static Bertrand competition.     

Network formation and stable equilibrium

We study the non-cooperative formation of a (directed) network that builds upon one-way immediate links. Our novel feature is that we require circular paths of links for productive activities. This captures more clearly the higher level of coordination that is often required for network formations than models such as those of Jackson and Wolinsky [A strategic model of social and economic networks, J. Econ. Theory 71 (1996) 44-74] and Bala and Goyal [A non-cooperative model of network formation, Econometrica 68 (2000) 1181-1229], in that in our model a single agent's unilateral action is limited in affecting the network structure. We completely characterize the class of Nash equilibria by showing that the minimality of a graph is both necessary and sufficient (Theorem 1). We also propose the concept of a stable network that is similar to the pairwise stability of Jackson and Wolinsky (1996). We show that stable equilibria are a wheel, a trivial network, or a sub-wheel partitioned network (Theorem 2). We modify the Bala and Goyal (2000) dynamic process with inertia, and obtain the convergence to stable equilibria regardless of the initial state (Theorem 3).     

The formation of networks with transfers among players

We examine the formation of networks among a set of players whose payoffs depend on the structure of the network, when players may bargain by promising or demanding transfer payments when forming links. We vary three aspects of the game: (i) whether players can only make transfers to (and receive transfers from) players to whom they are directly linked, or whether they can also subsidize links that they are not directly involved in, (ii) whether or not transfers relating to a given link can be made contingent on the full resulting network or only on the link itself, and (iii) whether or not players can pay other players to refrain from forming links. We characterize the networks that are supported under these variations and show how each of the above aspects either accounts for a specific type of externality, or deals with the combinatorial nature of network payoffs.     

Optimal dynamic risk sharing when enforcement is a decision variable

Societies provide institutions that are costly to set up, but able to enforce long-run relationships. We study the optimal decision problem of using self-governance for risk sharing or governance through enforcement provided by these institutions. Third-party enforcement is modelled as a costly technology that consumes resources, but permits the punishment of agents who deviate from ex ante specified allocations. We show that it is optimal to employ the technology whenever commitment problems prevent first-best risk sharing and fixed costs are sufficiently low, but never optimal to provide incentives exclusively via this technology. Commitment problems then persist and the optimal incentive structure changes dynamically over time with third-party enforcement monotonically increasing in the relative inequality between agents.     

Size approval voting

We propose a new class of voting procedures, called Size Approval Voting, according to which, the effective weight of a vote from a given individual depends on how many other candidates that individual votes for. In particular, weights are assumed to be non-negative and weakly decreasing in the number of approved candidates. Then, for a given profile of individual votes, all candidates with the maximal sum of weighted votes are elected. We show in our axiomatic analysis that the family of all Size Approval Voting procedures is characterized by a set of natural properties.     

Competitive prices as optimal cartel prices

In a linear oligopoly model with antitrust enforcement, the optimal cartel price converges to the competitive equilibrium price. The set of sustainable cartel prices does not shrink to the competitive price. We identify necessary conditions for this counter-intuitive convergence result.     

Collusion as public monitoring becomes noisy: Experimental evidence

This paper uses laboratory experiments to test the implications of the theory of repeated games on equilibrium payoffs and estimate strategies in an infinitely repeated prisoners' dilemma game with imperfect public monitoring. We find that subjects' payoffs (i) decrease as noise increases, and (ii) are lower than the theoretical maximum for low noise, but exceed it for high noise. Under the assumption that the subjects' strategy uses thresholds on the public signal for transition between cooperation and punishment states, we find that the best fitting strategy simply compares the most recent public signal against a single threshold.     

Strategic Tax Competition in Switzerland: Evidence from a Panel of the Swiss Cantons

Abstract. Tax competition is discussed as a source of inefficiency in international taxation and in fiscal federalism. Two preconditions for the existence of such effects of tax competition are that mobile factors locate or reside in jurisdictions with – ceteris paribus – lower tax rates, and that taxes are actually set strategically in order to attract mobile production factors. It is well known from studies about Swiss cantonal and local income tax competition that Swiss taxpayers reside where income taxes are low. In this paper, empirical results on strategic tax setting by cantonal governments are presented for a panel of the Swiss cantons from 1984 to 1999. Completing the evidence on Swiss tax competition, income tax rates in cantons are the lower, the lower the tax rates of their neighbors.     

Sorting equilibrium in a multi-jurisdiction model

This paper analyzes a general model of an economy with heterogeneous individuals choosing among two jurisdictions, such as towns or political parties. Each jurisdiction is described by its constitution, where a constitution is defined as a mapping from all possible population partitions into the (possibly multidimensional) policy space. This study is the first to establish sufficient conditions for existence of sorting equilibria in a two-jurisdiction model for a policy space of an arbitrary dimension.     

Bargaining foundations of the median voter theorem

We give a game-theoretic foundation for the median voter theorem in a one-dimensional bargaining model based on Baron and Ferejohn's [D. Baron, J. Ferejohn, Bargaining in legislatures, Amer. Polit. Sci. Rev. 83 (1989) 1181-1206] model of distributive politics. We prove that as the agents become arbitrarily patient, the set of proposals that can be passed in any pure strategy, subgame perfect equilibrium collapses to the median voter's ideal point. While we leave the possibility of some delay, we prove that the agents' equilibrium continuation payoffs converge to the utility from the median, so that delay, if it occurs, is inconsequential. We do not impose stationarity or any other refinements. Our result counters intuition based on the folk theorem for repeated games, and it contrasts with the known result for the distributive bargaining model that as agents become patient, any division of the dollar can be supported as a subgame perfect equilibrium outcome.     

A three-player dynamic majoritarian bargaining game

We analyze an infinitely repeated divide-the-dollar bargaining game with an endogenous reversion point. In each period a new dollar is divided among three legislators according to the proposal of a randomly recognized member—if a majority prefer so—or according to previous period's allocation otherwise. Although current existence theorems for Markovian equilibria do not apply for this dynamic game, we fully characterize a Markov equilibrium. The equilibrium is such that irrespective of the discount factor or the initial division of the dollar, the proposer eventually extracts the whole dollar in all periods. We also show that proposal strategies are weakly continuous in the status quo that equilibrium expected utility is not quasi-concave, and the correspondence of voters’ acceptance set (the set of allocations weakly preferred over the status quo) fails lower hemicontinuity.     

A necessary and sufficient condition for non-emptiness of the core of a non-transferable utility game

It is well-known that a transferable utility game has a non-empty core if and only if it is balanced. In the class of non-transferable utility games balancedness or the more general π-balancedness due to Billera (SIAM J. Appl. Math. 18 (1970) 567) is a sufficient, but not a necessary condition for the core to be non-empty. This paper gives a natural extension of the π-balancedness condition that is both necessary and sufficient for non-emptiness of the core.     

Equilibrium binding agreements: a comment

To construct their Equilibrium Binding Agreements, Ray and Vohra (J. Econ. Theory, 73 (1997) 30-78) define a concept of an equilibrium between coalitions and prove its existence for any coalition structure. We show that this result crucially depends on the quasi-concavity of the utility functions, which in turn depends on the type of mixed strategies used by the coalitions. When coalitions use uncorrelated mixed strategies utility functions may not be quasi-concave and an equilibrium may not exist. However, if coalitions use correlated strategies, an equilibrium always exist.     

An evolutionary approach to learning in a changing environment

The evolutionary fitness of the ability to learn a best response (at a cost) is explored in an environment where the underlying game changes stochastically over time. We provide a sufficient condition for asymptotic dominance by the learners. It does not require that the learners are the most fit type in any single state of the environment. We identify a necessary and sufficient condition that ensures the survival of the learners when learning costs are small. Last, we describe a medium-run phenomenon where the learners “spike”—their share temporarily rises and gets arbitrarily close to one following a regime shift.     

Transferable utility games with uncertainty

We introduce the concept of a TUU-game, a transferable utility game with uncertainty. In a TUU-game there is uncertainty regarding the payoffs of coalitions. One out of a finite number of states of nature materializes and conditional on the state, the players are involved in a particular transferable utility game. We consider the case without ex ante commitment possibilities and propose the Weak Sequential Core as a solution concept. We characterize the Weak Sequential Core and show that it is non-empty if all ex post TU-games are convex.     

Voluntary formation of communities for the provision of public projects

In this paper we examine a group formation problem, where heterogeneous individuals partitioned themselves into communities, each choosing its own public project from the given space of feasible projects. The model is that of “horizontal product differentiation” where individuals display distinct preferences over the policy space. We consider the notion of “efficient” configuration that minimizes the total project-related costs and aggregate personalized costs of all individuals, and “sustainable” configurations, those are immune against breakaways by subgroups of individuals. Our main result is that, with a unidimensional project space and single-peaked personalized costs, every efficient partition is sustainable.     

Nonminimal product differentiation as a bargaining outcome

It is well known that in a duopoly model of product choice with quadratic transportation cost, the firms locate at the extreme endpoints of the market. Jehiel (1992, Int. J. Ind. Organ, 10, 633–641) has examined this model in an infinite horizon setting where in the initial period the firms choose location and in subsequent periods charge the Nash bargaining solution prices. Then, in the unique equilibrium both firms locate at the center of the market. This paper examines the case when the firms instead charge the prices determined by either the egalitarian bargaining solution or the Kalai–Smorodinski bargaining solution. It is shown that central agglomeration is an equilibrium. Furthermore, there is a continuum of symmetric equilibria in addition where the firms locate apart from each other. So the products are not necessarily minimally differentiated. Thus different bargaining solutions provide quite different outcomes.     

Preemption in a real option game with a first mover advantage and player-specific uncertainty

In this paper a two-player real option game with a first-mover advantage is analyzed, where payoffs are driven by a player-specific stochastic state variable. It is shown that there exists an equilibrium which has qualitatively different properties from those in standard real option games driven by common stochastic shocks. The properties of the equilibrium are four-fold: (i) preemption does not necessarily occur, (ii) if preemption takes place, the rent-equalization property holds, (iii) for almost all sample paths it is clear ex-ante which player invests first, and (iv) it is possible that both players invest simultaneously, even if that is not optimal. It is argued from simulations that real option games with a common one-dimensional shock do not provide a good approximation for games with player-specific uncertainty, even if these are highly correlated.