Rational Coordination in Games with Enriched Representations

Abstract

We consider pure win-lose coordination games where the representation of the game structure has additional features that are commonly known to the players, such as colouring, naming, or ordering of the available choices or of the players. We study how the information provided by such enriched representations affects the solvability of these games by means of principles of rational reasoning in coordination scenarios with no prior communication or conventions.

Rational coordination with no communication or conventions

“…• Another natural extension of the present framework is to consider non-structural principles based on limited preplay communication and use of various types of nonstructural conventions based on some additional features of the game representation, e.g., partial priority orders of players, colours of choices, etc. For a general exploration of WLC games with enriched game representation see [11].…”

“…It is worth noting that if we considered a framework where WLC games were presented so that the names of the choices and players could always be used to uniquely define an ordering (of the players and their choices), solving games could be trivialised by using the pre-negotiated agreement to always choose the lexicographically least tuple from the winning relation. For more on solving coordination games with names or ordering of choices, see [11].…”

“…Note that we do not give a formal definition of an ideally rational rational agent. It is taken to be a philosophical primitive that is central to our study, but yet a notion that we cannot define formally in this paper 11 . Note also that, since purely rational principles are indeed followed by all ideally rational agents, such principles are not based on any particular conventions.…”

“…The work of Raine Rönnholm was partly supported by Jenny and Antti Wihuri Foundation. We thank the reviewers of this paper, as well as the reviewers of [13], [12], and [11], for helpful remarks and references.…”

The Optimal Way to Play the Most Difficult Repeated Coordination Games

“…However, similar work exists, the most notable example being the seminal article [6] that studies a generalization of WLC-games in a framework that has some similarities with our setting. Also the papers [8], [10], [7], [9] have a similar focus, as they also concentrate on coordination games with discrete win-lose outcomes. However, the papers [8], [10], [7], [9] do not investigate optimality of protocols in repeated games, unlike the current paper.…”