New research | Solid outcomes in finite games
In their article in the Journal of Economic Theory, Professor Jörgen Weibull, and co-authors introduce a concept they call “solid outcomes.” It’s designed to improve predictions in situations where different individuals, companies or organizations interact and each tries to make the best possible move, knowing others are doing the same.
In economics and related fields, this kind of situation is studied using game theory and also this study uses game theory. But many traditional methods have a problem: they often give too many possible outcomes or are overly sensitive to small, irrelevant details in how a situation is described. As a result, they can be hard to apply when trying to understand and predict real-world behavior.
The new approach avoids these issues. Solid outcomes are stable, consistent, and can be calculated efficiently. They are invariant under strategically irrelevant transformation of the game. The approach is a refinement of Nash equilibrium and is expressed in terms of observable outcomes rather than in strategies.
In short, the idea of solid outcomes offers a more reliable and precise way to anticipate what people will do when their decisions depend on one another.
Link to the publication
Abstract
A new solution concept for finite games is presented and analyzed. It is defined in terms of outcomes—probability distributions over the plays of the game. Solid outcomes are robust to the representation of the game, whether in normal or extensive form, and are consistent with backward induction. They are also unaffected by the removal or addition of dominated strategies. Solid outcome sets exist in all finite extensive-form games with perfect recall. They have support in minimal “game blocks,” a class of product sets of pure-strategy profiles that are robust set-valued candidates for conventions and social norms in recurrent population play of the game. Algorithms for identifying all solid outcomes are presented, and simulations illustrate the solution concept's significant cutting power and computational efficiency.
