Endogenous timing game with non-monotonic reaction functions

The aim of this paper is to generalize the endogenous timing game proposed by Hamilton and Slutsky (1990) to cases where the reaction functions are non-motononic, as for instance in the literature on contest. Following the taxonomy of social dilemma provided by Eaton (2004) we consider several pos- sible situations depending on the nature of interactions (plain complementarity or plain substituability and strategic complementarity or strategic substitutability). Under the assumptions of the existence and the uniqueness of the Nash and Stackelberg equilibria, we highlight the presence of a first-mover advantage or a second-mover incentive only depending on the nature of cross-effects in players’ payoff functions and the slopes of their reaction functions at the Nash equilibrium of the static game. These properties allow us to determine rigorously the Subgame Perfect Nash Equilibrium (SPNE) in the ten studied situations. We establish under which conditions on the nature of interactions a leader emerges at the SPNEfirst-mover advantage, endogenous timing game, second-mover incentive, Subgame Perfect Nash Equilibrium

An evasion game model for duopoly competition

Based on the Bertrand and Cournot economic models, we develop an evasion game model for a duopoly market with two players competing on price and quantity. We show that if the total financial strength of first mover is greater than that of the second mover, and the first mover observes the second mover perfectly, our proposed optimal strategy can be followed by the first mover to remain the market leader ahead of all competition

The Cournot outcome as the result of price competition

In a homogeneous product duopoly with concave revenue and convex costs we study a two stage game in which, first, firms engage simultaneously in capacity (production) and, after production levels are made public, there is sequential price competition in the second stage. Randomizing the order of play in the price subgame, we can find: (i) that the Cournot outcome can be sustained as a pure strategy subgame perfect Nash equilibrium (SPNE) of the whole game, (ii) a SPNE in which firms produce strictly more than the Cournot outcome.subgame perfect Nash equilibrium ; price ; quantity ; pure strategies ; Cournot

Managerial Incentives and Stackelberg Equilibria in Oligopoly

The paper investigates both quantity and price oligopoly games in markets with a variable number of managerial and entrepreneurial firms which defines market structure. Following Vickers (Economic Journal, 1985) which establishes an equivalence between the equilibrium under unilateral delegation and the Stackelberg quantity equilibrium, the outcomes of these games are compared with the ones in sequential multi-leaders and multi-followers games. The profitability of a managerial/entrepreneurial attitude vs leadership/followership is shown to critically depend upon the kind of strategy, price or quantity, and upon the assumed market structure. Indeed, the latter turns out to be crucial in determining the equivalence result that is shown to be contingent on the assumption that just one leader or one managerial firm operate in the market. A welfare analysis finally highlights the differences between the delegation and the sequential games, focusing on the impact of market structure and imperfect substitutability on the equilibria of the two games.Strategic delegation, sequential games, quantity and price competition, welfare analysis.

Leadership in Public Good Provision: a Timing Game Perspective

We address in this paper the issue of leadership when two governments provide public goods to their constituencies with cross border externalities as both public goods are valued by consumers in both countries. We study a timing game between two different countries: before providing public goods, the two policymakers non-cooperatively decide their preferred sequence of moves. We establish conditions under which a first- or second-mover advantage emerges for each country, highlighting the role of spillovers and the strategic complementarity or substitutability of public goods. As a result we are able to prove that there is no leader when, for both countries, public goods are substitutable. When public goods are complements for both countries, both countries may emerge as the leader in the game. Hence a coordination issue arises. We use the notion of risk-dominance to select the leading government. Lastly, in the mixed case, the government for whom public goods are substitutable becomes the leader.public good, Spillovers, Subgame Perfect Equilibrium, Strategic Complements, Stackelberg, Pareto Dominance, Risk Dominance

Leadership in Public Good Provision: a Timing Game Perspective

We address in this paper the issue of leadership when two governments provide public goods to their constituencies with cross border externalities as both public goods are valued by consumers in both countries. We study a timing game between two different countries: before providing public goods, the two policymakers non-cooperatively decide their preferred sequence of moves. We establish conditions under which a first- or second-mover advantage emerges for each country, highlighting the role of spillovers and the strategic complementarity or substitutability of public goods. As a result we are able to prove that there is no leader when, for both countries, public goods are substitutable. When public goods are complements for both countries, both countries may emerge as the leader in the game. Hence a coordination issue arises. We use the notion of risk-dominance to select the leading government. Lastly, in the mixed case, the government for whom public goods are substitutable becomes the leader.public good;Spillovers;Subgame Perfect Equilibrium;Strategic Complements;Stackelberg;Pareto Dominance;Risk Dominance

Endogenous Timing in Strategic Environmental Policymaking

In this paper, we endogenize the timing of policymaking in a simple two-country model of strategic environmental policy. We consider a timing game in which two policymakers non-cooperatively decide their preferred sequence of moves before setting emission tax rates. We show that whether the policymakers implement emission tax policies simultaneously or sequentially crucially depends on the magnitude of environmental damages: When the damages are insignificant, the tax rates are strategic substitutes and the simultaneous-move policymaking emerges in equilibrium. In contrast, when the damages are significant, the tax rates are strategic complements and the sequential-move policymaking emerges. In addition, we extend the model by allowing for differences in the vulnerability to environmental damages between countries. When the differences are large, the unique equilibrium of the game is the situation where the less vulnerable country acts as a leader. In the case where multiple equilibrium emerges, the risk dominant equilibrium is also that the less vulnerable country leads.Strategic environmental policy; Endogenous timing; Environmental tax; Duopoly