The AND-OR game: Equilibrium Characterization (Working Paper)

We consider a simple simultaneous first price auction for multiple items in a complete information setting. Our goal is to completely characterize the mixed equilibria in this setting, for a simple, yet highly interesting, {\tt AND}-{\tt OR} game, where one agent is single minded and the other is unit demand.

💡 Research Summary

The paper studies a simple simultaneous first‑price auction for two items under complete information, focusing on the “AND‑OR” game. In this game one player (the AND player) derives value 1 only if she wins both items, while the other player (the OR player) derives value v > ½ from winning any single item (or both). Bids are submitted simultaneously for each item; the highest bid wins the item and the winner pays her bid. The authors first observe that when v > ½ no pure Nash equilibrium exists, because any pure profile can be profitably deviated from by either player.

A specific mixed‑strategy equilibrium previously identified in Hassidim et al.