Topological ordering of a list of randomly-numbered elements of a network
Communications of the ACM
Topological sorting of large networks
Communications of the ACM
The Art of Computer Programming, 2nd Ed. (Addison-Wesley Series in Computer Science and Information
The Art of Computer Programming, 2nd Ed. (Addison-Wesley Series in Computer Science and Information
Interactive Theorem Proving and Program Development
Interactive Theorem Proving and Program Development
A constructive approach to sequential Nash equilibria
Information Processing Letters
Subgame perfection for equilibria in quantitative reachability games
FOSSACS'12 Proceedings of the 15th international conference on Foundations of Software Science and Computational Structures
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In a game from game theory, a Nash equilibrium (NE) is a combination of one strategy per agent such that no agent can increase its payoff by unilaterally changing its strategy. Kuhn proved that all (tree-like) sequential games have NE. Osborne and Rubinstein abstracted over these games and Kuhn's result: they proved a sufficient condition on agents' preferences for all games to have NE. This paper proves a necessary and sufficient condition , thus accounting for the game-theoretic frameworks that were left aside. The proof is formalised using Coq, and contrary to usual game theory it adopts an inductive approach to trees for definitions and proofs. By rephrasing a few game-theoretic concepts, by ignoring useless ones, and by characterising the proof-theoretic strength of Kuhn's/Osborne and Rubinstein's development, this paper also clarifies sequential game theory. The introduction sketches these clarifications, while the rest of the paper details the formalisation.