On coordination and coordination games

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“Both the organization theorist Chester Barnard and the economist Friedrich Hayek took adaptation to be the main purpose of economic organization, but with differences.” — Oliver Williamson Nobel Lecture

Coordination has become an increasingly important C-word in business and economics, based on the emerging realization that not all economic activity can be orchestrated via control (in enterprises) or competition (across markets). But what is coordination really about?

Picture by Josh Calabrese.

Unlike cooperation, which has taken on the meaning of “solving the Prisoner’s Dilemma” and collaboration, which just generically means “working together”, coordination suffers from being vaguely defined, which often means one has to divine the type of coordination implied.

Daniel Klein and Aaron Orsborn recently offered an intriguing pointer: the meaning of coordination has shifted over time, from longitudinal alignment (concatenation of tasks) to simultaneous alignment (synchronization of tasks).

The traditional definition, which focuses on longitudinal contingencies (and is likely also the definition Chester Barnard had in mind), is the traditional purview of production — in today’s parlance: supply chain — typically captured in machine scheduling models: try to bring the existing tasks into the right order.

The modern definition, ascribed to Thomas Schelling, focuses on synchronous (mis)alignment in the absence of communication. There is a standard game in game theory known as “pure coordination”, but it comes with variants, some but not all of which are usually summarized under the bracket of coordination games.

Most of the modern coordination game literature starts from a specific type of (2-player) game and scales from there. As it turns out, they’re all closely related. The commonality is that aside from receiving a benefit from taking an action, there is also a benefit (or sometimes a penalty) to be reaped from taking the same action as others. Hence, coordination.

Just to offer some of the most famous games bracketed under coordination games:

Battle of the sexes is coordination with goal conflict.

Stag hunt is coordination under nonparticipation risk.

Tragedy of the commons is anti-coordination or crowding game.

Matching pennies, also known as pesky little brother is an asymmetric coordination/anti-coordination game.

The world of coordination games is rich and fascinating, but most of the fascination hinges on understanding the context. The original building block is actually quite boring. Written in a particular way, it is a common prisoner’s dilemma game with the temptation of selfish motives removed.

Coordination Game (T=0) vs Prisoner’s Dilemma (T=4).

The reason why it’s boring is that as a one-shot game it has an obviously dominant, symmetric, Nash, Pareto-optimal strategy set: CC. It only becomes interesting if we add context, e.g. how do both players get from DD to CC without communicating?

In the world of operations research, the problem of moving from D to C is known as machine replacement problem. When to invest in a new technology that could produce more efficiently, when switching is costly? In economics, the problem of coordinated machine replacement has an even wider scope. It’s also known as Innovation. When to compel everyone to switch to a new technology?

A reason for this is that coordination underpins the important concept of mutuality (of the Williamsonian trifecta conflict-mutuality-order). Mutual action is always preferred by all parties. Except the risks and rewards of finding such a mutual solution are not always equally distributed.

Sometimes symmetry or asymmetry of risks and rewards can be the driver, sometimes it can be an obstacle to this process of reaching a higher state called “innovation”.

From this it is just a small step to realizing that timing is a major driver of coordination success or failure, and thus we’re back to the Barnard-type coordination as intertemporal concatenation of activities.

Just before introducing his famous markets-as-beauty-contest metaphor, John Maynard Keynes wrote about endogenous timing games: markets-as-musical-chairs.

From John Maynard Keynes’ General Theory.

But what is a concatenation failure in the sense of Chester Barnard? We experience it every day when we take multiple buses or trains to reach a destination. If we have a sequence of buses 1–2–3–4, only one bus has to be late for our whole trip to be out of whack. Another word for this is a Forrester shock.

A key point is that the cost of such a system failure can dwarf the individual cost of a single failure due to accelerating upstream and downstream knock-on effects (externalities). This gave rise to concepts like opportunism and holdup. And a resolution concept called contract.

At the juncture of Barnard’s longitudinal concatenation and Schelling’s simultaneous synchronization we have a different set of ideas on how to coordinate: The Hayek-Coase spontaneous, polycentric or decentralized coordination. In operations research we would call it multi-machine scheduling.

Whether it was expanding industrialization or transportation or the emerging socialist calculation debate, the folks at LSE realized that coordination happens at the intersection between contingent (concatenated) and simultaneous action. Thomas Schelling would’ve agreed.