The Coordination

Several arrangements can serve everyone while none tells us how to arrive there together. The earlier Collected Coordination began with the side of the road: either side can serve in an otherwise symmetric world, provided the drivers agree. Once traffic is moving, each driver has an excellent reason to follow its convention; before a convention exists, that reason leaves a choice unresolved. Which technical standard, which language of trade, which meeting place — the gain from convergence does not necessarily select its destination. Here the difficulty of cooperation takes a different form from the dilemma. An agreed arrangement can already be an equilibrium, with nobody wanting to depart alone. What remains to be explained is how separate people, considering one another’s choices, come to inhabit the same arrangement. The good answer can be plural even when the action must be common.

The symmetry becomes visible in a small invented game in which two strangers must choose the same door. There are two doors, East and West; each person receives six units of satisfaction if their choices match and zero if they differ. East with East and West with West are both equilibria. Either participant, finding the other at East, would lose by moving alone; the same reasoning holds at West. Independently tossing fair coins makes them meet only half the time, for an expected return of three each. A single public coin, with a shared rule assigning its result to a door, could make them meet every time if both follow the rule. The gain comes from linking their choices. Nothing about the original rewards supplies that link, and describing the two successful outcomes as equilibria has not yet explained which door the strangers will open.¹

A focal point supplies a clue by making one answer stand out as the answer the other person might also recognize. Schelling’s meeting problem asked people to name a place and time in New York without consulting their partners. In his expressly unscientific sample, Grand Central’s information booth and noon attracted the answers; he also noted that the sample’s New Haven setting might matter. The lesson lies in the relation between recognition and expectation. My favourite café will not help if you have never heard of it. A conspicuous landmark may help if each of us expects its conspicuousness to matter to the other. Such clues can come from a unique object, a familiar name or a shared occasion. They depend on a history outside the numerical rewards, and two people with different histories may see different answers as obvious. The focal point works through the expectation that its visibility is shared.²

A convention carries an answer forward so that each new participant need not invent it again. Hume pictured two people pulling the oars of a boat without having exchanged promises: each action refers to the other, and the shared interest becomes known through their conduct. He extended the argument to practices that gain force gradually, as experience teaches people what to expect. In the world of the earlier plate, the customary gauge and the language of the room perform this work. An inherited rule can make coordination inexpensive to each person who adopts it, because the difficult act of selection has already occurred. Yet the same expectation can make change difficult. In an imagined network whose machines all use one connector, the owner who installs an incompatible replacement alone loses access to the others. A proposed improvement must therefore answer a second question: how will the users move together?³

A common interest in agreement can coexist with a dispute about who benefits most from it. Alter the doors so that meeting at East gives the first person six and the second five, while meeting at West reverses those rewards; a mismatch still gives both zero. Both would rather meet than fail, but each favours a different meeting. The first game’s symmetry has acquired a distributive question, and a familiar label now competes with the attraction of a larger share. Crawford, Gneezy and Rottenstreich found this fragility in their one-shot coordination experiments: even small payoff asymmetries could sharply reduce coordination when the attraction of the labels conflicted with the payoffs. Some of their other treatments retained strong coordination despite asymmetry. A salient answer can therefore help settle a disagreement without commanding every setting. The visible meeting place does not erase what each participant stands to gain by meeting elsewhere.⁴

A public rule can make the route to coordination more definite, provided people have reason to expect that it will be followed. Return to the imagined connector: a published standard, an announced changeover date and a credible plan for making the necessary replacements could give each owner evidence about the others’ next move. These arrangements answer different parts of the difficulty. The standard specifies the destination; the timetable specifies when to move; the replacements make compliance feasible. A command backed by penalties would also alter the rewards of refusing, while assistance with replacement would alter the cost of joining. Institutions can work through several of these channels at once. Their success cannot be inferred from the clarity of the announcement alone. A perfectly legible plan that the users cannot afford to implement may leave everyone waiting beside a machine that no longer connects.⁵

When several outcomes would suit everyone, a shared history, a recognizable clue or a public arrangement can bring their expectations to the same one. Each gives people something on which to condition their conduct; none follows merely from the existence of mutual gains. That is why an established convention can feel as solid as the landscape while depending on the expectation that others will continue to respect it. It is also why the success of coordination leaves questions of distribution and change open. An arrangement may be easy to anticipate, difficult to leave and costly for some of the people who sustain it. To explain how they meet is already to explain a considerable part of social order. To decide whether this is where they ought to meet requires a further account of their alternatives, their burdens and their power to choose another destination.