TY - JOUR

T1 - Equilibria in a class of aggregative location games

AU - Harks, T.

AU - Klimm, M.

PY - 2015/1/1

Y1 - 2015/1/1

N2 - Consider a multimarket oligopoly, where firms have a single license that allows them to supply exactly one market out of a given set of markets. How does the restriction to supply only one market influence the existence of equilibria in the game? To answer this question, we study a general class of aggregative location games where a strategy of a player is to choose simultaneously both a location out of a finite set and a non-negative quantity out of a compact interval. The utility of each player is assumed to depend solely on the chosen location, the chosen quantity, and the aggregated quantity of all other players on the chosen location. We show that each game in this class possesses a pure Nash equilibrium whenever the players’ utility functions satisfy the assumptions negative externality, decreasing marginal utility, continuity, and Location–Symmetry. We also provide examples exhibiting that, if one of the assumptions is violated, a pure Nash equilibrium may fail to exist.

AB - Consider a multimarket oligopoly, where firms have a single license that allows them to supply exactly one market out of a given set of markets. How does the restriction to supply only one market influence the existence of equilibria in the game? To answer this question, we study a general class of aggregative location games where a strategy of a player is to choose simultaneously both a location out of a finite set and a non-negative quantity out of a compact interval. The utility of each player is assumed to depend solely on the chosen location, the chosen quantity, and the aggregated quantity of all other players on the chosen location. We show that each game in this class possesses a pure Nash equilibrium whenever the players’ utility functions satisfy the assumptions negative externality, decreasing marginal utility, continuity, and Location–Symmetry. We also provide examples exhibiting that, if one of the assumptions is violated, a pure Nash equilibrium may fail to exist.

U2 - 10.1016/j.jmateco.2015.09.006

DO - 10.1016/j.jmateco.2015.09.006

M3 - Article

VL - 61

SP - 211

EP - 220

JO - Journal of Mathematical Economics

JF - Journal of Mathematical Economics

SN - 0304-4068

ER -