# Games for cautious players: the equilibrium in secure strategies

Working paper

Issue number:

2016/51

Series:

CORE Discussion Papers

Publisher:

Université Catholique de Louvain

Year:

2016

A non-cooperative solution, the Equilibrium in Secure Strategies (EinSS), is defined
that extends the Nash equilibrium in pure strategies when it does not exist and is
meant to solve games where players are "cautious", i.e. looking for secure positions
and avoiding threats. This concept abstracts and unifies various ad hoc solutions
already formulated in various applied economic games that have been discussed
extensively in the literature. It complements usefully mixed strategy Nash equilibria
that are usually not explicit and difficult to interpret in these games. Like the Nash
equilibrium, the EinSS is a static concept, and the basic requirement of excluding at
equilibrium some deviations remains. But it also appeals to dynamic intuitions,
tolerating at equilibrium the possibility of some deviations, which would be blocked by
counter-deviations punishing the deviator. This is in line with the "objection-counterobjection"
rationale first introduced in cooperative games. A general existence
theorem is provided and then applied to the price-setting game in 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 Rothchild-StiglitzWilson
contract shown to be an EinSS even when the Nash equilibrium breaks down.