Deadlock (game theory)

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

In game theory, Deadlock is a game where the action that is mutually most beneficial is also dominant. (An example payoff matrix for Deadlock is pictured to the right.) This provides a contrast to the Prisoner's Dilemma 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).

References

• GameTheory.net
• C. Hauert: Effects of space in 2 x 2 games. Int. J. Bifurc. Chaos 12 (2002) 1531-1548.
• H.-U. Stark: Dilemmas of partial cooperation. Evolution 64 (2010) 2458–2465.