Theoretical Economics 17 (2022), 617–650

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### Games with switching costs and endogenous references

*Begum Guney, Michael Richter*

#### Abstract

We introduce a game-theoretic model with switching costs and endogenous references. An agent endogenizes his reference strategy and then, taking switching costs into account, he selects a strategy from which there is no profitable deviation. We axiomatically characterize this selection procedure in one-player games. We then extend this procedure to multi-player simultaneous games by defining a Switching Cost Nash Equilibrium (SNE) notion, and prove that (i) an SNE always exists; (ii) there are sets of SNE which can never be a set of Nash Equilibrium for any standard game; and (iii) SNE with a specific cost structure exactly characterizes the Nash Equilibrium of nearby games, in contrast to Radner's (1980) $\varepsilon$-equilibrium. Subsequently, we apply our SNE notion to a product differentiation model, and reach the opposite conclusion of Radner (1980): switching costs for firms may benefit consumers. Finally, we compare our model with others, especially K\"{o}szegi and Rabin's (2006) personal equilibrium.

Keywords: Switching cost Nash equilibrium, choice, endogenous reference, switching costs, epsilon equilibrium

JEL classification: D00, D01, D03, C72

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