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# Coordination Failure

EXAMPLES OF COORDINATION FAILURE

BIBLIOGRAPHY

The notion of coordination failure can be understood by considering the simple coordination game in Table 1. In this game, Player 1 and Player 2 simultaneously and independently choose action A or B. The numbers in the table represent the payoffs associated with the different outcomes of interaction. If both players choose option A, both get a payoff of 1, if both choose B, they both get a payoff of 2, and if one player chooses A and the other B, the one who chose A gets 1, the other gets 0.

Coordination games, as outlined by Russell Cooper in his 1999 work, are characterized by multiple equilibria. In the following example, both players choosing A and

Table 1
A coordination game
Player 2
AB
Player 1A1,11,0
B0,12,2

both players choosing B are equilibria (in addition, there is a mixed-strategy equilibrium in which both players choose A and B with a probability of ½). These equilibria are Pareto-ranked, meaning that both players are better off in one equilibrium than in the other. In the example, both players are better off if they coordinate on action B than if they coordinate on action A.

Coordination failure prevails if players coordinate on the inefficient equilibrium (here: both choose A). Coordination failure is an equilibrium phenomenon because given that one player chooses A, it is in the interest of the other player (i.e., it is a best reply) to also choose A. In colloquial language, the failure to coordinate on any equilibrium is sometimes also called coordination failure. It is more precise to talk about miscoordination in this case because a non-equilibrium phenomenon is concerned.

Coordination failure suggests an efficiency-enhancing role for policy intervention and collective action. If agents are in a Pareto-inferior equilibrium, individuals cannot move to the superior equilibrium by individual action (lock-in effect). In contrast, a coordinated move is necessary to reach a Pareto-superior equilibrium.

Coordination failure arises because of strategic uncertainty, not because a conflict of interest prevails. While choosing B is attractive because it possibly yields a higher payoff, it is also risky to choose B. If one player is uncertain that the other player will choose B, he might choose the safe option A. Therefore, confidence and expectations are important determinants of coordination failure.

Multiple equilibria arise in coordination games because of strategic complementarity, meaning that the optimal decision of one agent is positively dependent on the decisions of other players. Coordination games also exhibit positive spillovers in that the payoffs of one player increase as the action by the other player increases (assuming that action B represents a higher level of activity than action A).

## EXAMPLES OF COORDINATION FAILURE

More elaborate versions of the coordination game in Table 1 with more than two players and two actions have been used to explain coordination failure in many contexts.

Teamwork Suppose two workers produce a joint output by providing costly effort and both are paid according to team output. Both workers are better off if both exert high effort (action B in the table) and coordination failure prevails if both provide low effort.

Education Acquiring education might be less profitable if others are not educated. If all agents expect others to acquire little education, investments in education might remain low.

Bank Runs If most creditors leave their savings in the bank, the bank is liquid and it is optimal to leave the savings in the bank. If all other creditors withdraw their savings, the bank becomes illiquid and it is best to also withdraw ones savings. A similar reasoning has been used to account for speculative currency attacks and decisions to refinance businesses on the verge of bankruptcy.

Search and Matching If few agents use a specific medium to search for a partner, the other players have little incentives to use this medium because of the low likeliness to find a good match in a thin market. Coordination failure might therefore explain low intensity of search for employment. A similar reasoning has been used to explain failure to adopt superior technological standards or languages. Applications in development economics emphasize path-dependence and lock-in, suggesting that an economy might be stuck in a development trap today because agents failed to coordinate, possibly due to historical accident, on a Pareto-superior equilibrium in the past.

Macroeconomics Coordination failure has many applications in macroeconomics. A classic example refers to investments and expectations of future output. If most firms expect future aggregate demand to be low, they invest little today. This, in turn, induces low aggregate demand today, which might be interpreted as confirming low expectations. A recession might therefore result from self-fulfilling expectations. The literature on sunspots suggests that expectations might be coordinated by irrelevant events or information. For example, leading indicators of macroeconomic activity might be particularly accurate as long as economic agents believe they are good indicators.

The empirical relevance of these examples is contested in the literature because theories of coordination failure are difficult to test in the field. Economists have therefore sought to test the determinants of coordination failure in a broad range of coordination games in the experimental laboratory. Experimental economists have investigated elaborate versions of the game in Table 1, pure coordination games (in which equilibria are equally good, i.e., not Pareto-ranked), and asymmetric games (in which agents coordinate on different actions).

Coordination problems are related to but distinct from cooperation problems. The coordination game in Table 1 is transformed into a cooperation game (a prisoners dilemma) if the payoffs in the lower left cell are changed to (0,3) and in the upper right cell to (3,0). Actions A and B are often called defection and cooperation. The resulting cooperation game has a unique and inefficient equilibrium [payoffs are (1,1)]. A rational and self-interested player chooses A (i.e., free-rides) irrespective of what the other player chooses in the cooperation game.

## BIBLIOGRAPHY

Camerer, Colin. 2003. Behavioral Game Theory: Experiments in Strategic Interaction. Princeton, NJ: Princeton University Press.

Cooper, Russell W. 1999. Coordination Games: Complementarities and Macroeconomics. Cambridge, U.K.: Cambridge University Press.

Fehr, Ernst, and Jean-Robert Tyran. 2007. Money Illusion and Coordination Failure. Games and Economic Behavior 58(2): 246268.

Mankiw, N. Gregory, and David Romer, eds. 1991. New Keynesian Economics: Coordination Failures and Real Rigidities. Vol. 2. Cambridge, MA: MIT Press.

Jean-Robert Tyran