Abstract
A simple expression is derived for the optimal strategy in the minimum effort game. This maps from player beliefs to an optimal effort level. From this expression the set of Nash equilibria in the game is fully characterized. All Nash equilibria are symmetric and involve at most two actions being played with positive probability. We discuss how our expression for the optimal strategy can help inform on the comparative statics of a change in the number of players and effort cost benefit ratio.
Highlights
IntroductionThe minimum effort game, known as the weak link game, is a stylized way to model the production of any good whose output depends on the weakest component of production
The minimum effort game, known as the weak link game, is a stylized way to model the production of any good whose output depends on the weakest component of production.Many goods have this property and so the game has been widely applied over the last thirty years or so
The key issue in the minimum effort game is that of equilibrium selection
Summary
The minimum effort game, known as the weak link game, is a stylized way to model the production of any good whose output depends on the weakest component of production. Our second main result (Theorem 2) provides a general expression for the optimal strategy in the minimum effort game This expression maps from a player’s beliefs to an optimal strategy and provides a very specific trade-off between optimal effort, the number of players and the cost benefit ratio. To put this result in context we highlight that surprisingly little is known about how changes in the costs and benefits of effort translate into behavior in the minimum effort game.
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