Sequential location in a discrete directional market with three or more players

This paper expands Lai’s (Reg Sci Urban Econ 31:535–546, 2001) directional market analysis to a three-player game and endogenizes a restricted assumption of Lai (Reg Sci Urban Econ 31:535–546, 2001) through the test of a validated equilibrium introduced by Spagat (Math Soc Sci 24:49–57, 1992) and the use of lexicographic preference relation players (with payoff ranking a secondary consideration after the game’s payoff). There are multiple equilibrium outcomes, and any player may take advantage in this game due to the indifference problem of the players. However, if we utilize the validated equilibrium refinement, then the results present that the later the players enter a directional market, the greater the benefits they receive. If a player’s preference relation is lexicographic ordering, then we obtain results identical to the validated equilibrium outcomes. This paper ends with an extension of a general number of players.