C	D
c	1, 1	0, 3
d	3, 0	2, 2

In game theory

Game theory

Game theory is a mathematical method for analyzing calculated circumstances, such as in games, where a person’s success is based upon the choices of others...

, Deadlock is a game where the action that is mutually most beneficial is also dominant

Dominance (game theory)

In game theory, strategic dominance occurs when one strategy is better than another strategy for one player, no matter how that player's opponents may play...

. (An example payoff matrix for Deadlock is pictured to the right.) This provides a contrast to the Prisoner's Dilemma

Prisoner's dilemma

The prisoner’s dilemma is a canonical example of a game, analyzed in game theory that shows why two individuals might not cooperate, even if it appears that it is in their best interest to do so. It was originally framed by Merrill Flood and Melvin Dresher working at RAND in 1950. Albert W...

 where the mutually most beneficial action is dominated. This makes Deadlock of rather less interest, since there is no conflict between self-interest and mutual benefit. The game provides some interest, however, since one has some motivation to encourage one's opponent to play a dominated strategy.

General definition

	C	D
c	a, b	c, d
d	e, f	g, h

Any game that satisfies the following two conditions constitutes a Deadlock game: (1) e>g>a>c and (2) d>h>b>f. These conditions require that d and D be dominant. (d, D) be of mutual benefit, and that one prefer one's opponent play c rather than d.

Like the Prisoner's Dilemma, this game has one unique Nash equilibrium: (d, D).