Santa Fe Institute

Unlearnable games: When game theory breaks down

Jan. 7, 2013 4:05 p.m.

For decades, economists have relied on game theory as a basis for understanding behaviors in financial markets. But these simplified models of decision-making assume the players fully understand the game, and rationally tend toward what is known as the Nash equilibrium point – the sweet spot of optimized win, risk, and tradeoff.

Such assumptions give far too much credit to decision makers in actual financial markets, who are rarely fully aware of either the rules or the other players’ choices, and who often make irrational choices. As a result, game theory does a poor job of representing real-life economics. When, then, is it time to abandon game theory and use other approaches?

Tobias Galla, a frequent SFI collaborator at the University of Manchester, and SFI External Professor Doyne Farmer, at the Institute for New Economic Thinking at Oxford, searched for the point at which game theory breaks down in modeling economic behavior. They ran thousands of simulations of two-person games in which each player had to choose among various moves repeatedly. Each move had many possible payoffs; players chose their best moves based on their successes and their recall of previous experience.

Their results are published this week in Proceedings of the National Academy of Science.

Galla and Farmer found three kinds of behaviors, depending on the complexity of the game. Zero-sum games, where the won and lost amounts sum to zero, lead to stable outcomes. In games with a competitive character, players’ strategies vary indefinitely, producing high-dimensional chaotic behavior. And in games of a more cooperative nature, players eventually settle into one of dozens of stable outcomes.

Finally, boosting players’ memories changed the outcome, in a surprising way: the more a player remembered past behavior, the less likely he or she was to repeat move sequences. In such cases, no pattern of response emerged, even with “experience-weighted attraction” – when players keep choosing previously successful strategies and avoiding bad or dicey options based on what they've learned the hard way. Instead, long memory tends to lead to unpredictable behaviors, and the outcome is what is known in theoretical physics as chaotic attractors.

The researchers conclude that equilibrium is not the right thing to look for in a game, noting that some games are inherently unlearnable. This supports the hypothesis that the real world is frequently not stable, and that equilibrium models are not that relevant for understanding decisions in a financial market.

The pair is looking to expand their study to multiplayer games and to cases in which the game itself changes with time. This is akin to situations in financial markets, where multiple players interact with and react to each other’s decision making, and where new strategies become available as time progresses.

Read the paper in PNAS (January 7, 2013, subscription required)

Read the article in Physorg (January 7, 2013)

Read the article in RedOrbit (January 8, 2013)

Read the article in Wired (January 8, 2013)

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