Games for cautious players: The Equilibrium in Secure Strategies

A non-cooperative solution, the Equilibrium in Secure Strategies (EinSS), is defined as an extension of the Nash equilibrium in pure strategies, and is meant to solve games where players are “cautious,” i.e., looking for secure positions and avoiding threats. This concept abstracts and unifies ad hoc solutions already formulated in various applied economic games that have been discussed extensively in the literature. A general existence theorem is provided and then applied to the price-setting game in the Hotelling location model, to Tullock's rent-seeking contests, and to Bertrand-Edgeworth duopoly. Finally, competition in the insurance market game is re-examined and the Rothschild-Stiglitz-Wilson contract is shown to be an EinSS even when the Nash equilibrium breaks down.