Abstract
Richman games are zero-sum games, where in each turn players bid in order to determine who will play next (Lazarus et al., 1999). We extend the theory to impartial general-sum two player games called bidding games, showing the existence of pure subgame-perfect equilibria (PSPE). In particular, we show that PSPEs form a semilattice, with a unique and natural Bottom Equilibrium. Our main result shows that if only two actions available to the players in each node, then the Bottom Equilibrium has additional properties: (a) utilities are monotone in budget; (b) every outcome is Pareto-efficient; and (c) any Pareto-efficient outcome is attained for some budget. In the context of combinatorial bargaining, we show that a player with a fraction of X% of the total budget prefers her allocation to X% of the possible allocations. In addition, we provide a polynomial-time algorithm to compute the Bottom Equilibrium of a binary bidding game.
Original language | English |
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Pages (from-to) | 166-193 |
Number of pages | 28 |
Journal | Games and Economic Behavior |
Volume | 112 |
DOIs | |
State | Published - Nov 2018 |
Keywords
- Bargaining
- Combinatorial games
- Extensive form games
- Richman games
All Science Journal Classification (ASJC) codes
- Finance
- Economics and Econometrics