Abstract
We introduce a non-cooperative game model in which players’ decision nodes are partially ordered by a dependence relation, which directly captures informational dependencies in the game. In saying that a decision node v is dependent on decision nodes v1,…,vk, we mean that the information available to a strategy making a choice at v is precisely the choices that were made at v1,…,vk. Although partial order games are no more expressive than extensive form games of imperfect information (we show that any partial order game can be reduced to a strategically equivalent extensive form game of imperfect information, though possibly at the cost of an exponential blowup in the size of the game), they provide a more natural and compact representation for many strategic settings of interest. After introducing the game model, we investigate the relationship to extensive form games of imperfect information, the problem of computing Nash equilibria, and conditions that enable backwards induction in this new model.
Highlights
The two most important game models in non-cooperative game theory are normal form games and extensive form games
As we are interested in the computational properties of partial order games, we introduce a compact representation for strategies and utility functions in partial order games, based on Boolean circuits, which enables us to investigate questions about their computational complexity
We study the relationship of our game model to other game models: partial order Boolean games [1], Multi-Agent Influence Diagrams (MAIDs) [2,3], and extensive form games of imperfect information
Summary
The two most important game models in non-cooperative game theory are normal form games and extensive form games. We analyse partial order games by means of Nash equilibrium—arguably game theory’s most prominent non-cooperative solution concept—and the solutions given by a natural backwards induction procedure for partial order games defined on the dependence relation. Our main result is to present a technique for translating partial order games into strategically equivalent extensive form games, this translation comes at the cost of an exponential blowup in the size of the game. This leads us into a discussion of the use of partial order games as a compact representation of extensive form games. We conclude with a brief discussion and pointers for future work
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