# Good Thinking

Ideas that influence the way we think.

# Rock-Paper-Scissors is Deeper Than You Thought

A recent study shows how people's preferred strategies can beat game theory.

As a child, many of us settled disputes (such as who would go first down the slide) by playing a simple game called Rock-Paper-Scissors. The game is simple: You pound your closed fist into your hand three times while chanting "rock-paper-scissors," then signal your choice by making a fist to represent "rock," pointing your index and middle fingers to represent "scissors," or opening your hand wide to represent "paper." The rule for winning was simple as well: Rock crushed scissors, scissors cut paper, and paper covered rock. If everyone made the same choice (everyone chose "rock"), it was a tie, and the game was played again until a winner emerged triumphant.

What you probably didn't know is that rock-paper-scissors is a fundamental non-cooperative game that has been widely used by game theorists to study competition phenomena as wide-ranging as species diversity of ecosystems and price dispersion in markets. Because no option is absolutely better than either of the others, a rational agent chooses one of the three options randomly on each round in order to avoid being predictable and therefore getting exploited by the other players. After all, if you always choose "rock," other players will figure this out and always choose "paper" in order to beat you. That means that each rational agent has a 1 out of 3 chance of winning on any given round. In game theory, this game structure is referred to as mixed strategy Nash Equilibrium. Game theory recently catapulted to national attention when Arthur Chu used it to win a series of Jeopardy games

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But evolutionary game theory based on the concept of bounded rationality predicts a different outcome: It predicts cyclic behavior—not random selectionespecially for finite populations. Economist Herbert Simon proposed the notion of bounded rationality to explain how what counts as rational depends on the information decision-makers have, the amount of time available to reach a decision, and the cognitive or computational limitations of their minds. This is a crucial concept because game theory and other economic models of rational decision making define it as optimization, that is, finding the optimal solution given unlimited time, resources, and computing capability. Decision-making rarely meets these conditions, and so people opt to simplify their choices and exploit environmental patterns (or contingencies) that allow then to arrive at a satisfactory—as opposed to optimal—solution. For this reason, human decision-making is often described as satisficing rather than optimizing. And, all told, this strategy frequently serves us pretty well.

A recent study looked at how people play rock-paper-scissors and discovered that, yes indeed, people behave more like biological satisficers than rational optimizers, adopting a cyclical strategy rather than the random choice strategy consistent with game theory. The surprising thing, however, is that this conditional response strategy actually turns out to yield better outcomes than game theory's mixed strategy Nash Equilibrium.

The researchers recruited a total number of 360 students from different disciplines of Zhejiang University and divided them into groups of 60. Each group then played 300 rounds of rock-paper-scissors (yes, three HUNDRED rounds). After the final game was played, the players were paid in cash proportional to their accumulated payoffs.

The researchers found that when players won a round using a particular choice (e.g., "rock"), they were more likely to stick with that winning option in the next round. But if they lost, they tended to switch to one of the other options, and the option they chose was consistent with what would beat the choice they had just made. So if "rock" had been chosen and was beaten by "paper," the player would try "paper" on the next round, and so on.

This means that the players' choices were conditional on what was played and the outcome of that choice. This "win-stay , lose-shift" strategy is known in game theory as a conditional response, and when playing with stable populations (as was done in this study), it turned out to be very successful: The conditional strategy outperformed the Nash Equilibrium mixed strategy in payoff by as much as 10 percent. The researchers referred to this "win-stay, lose shift" strategy as "socially efficient." It is also sometimes referred to as a "Pavlov strategy," and it has been shown to facilitate cooperation in Prisoners Dilemma games.

Even more interesting is that similar cycling patterns were observed in related studies with games that employed more than three options…such as rock-paper-scissors-lizard-spock.

Copyright May 2, 2014 Dr. Denise Cummins

Dr. Cummins is a research psychologist, a Fellow of the Association for Psychological Science, and the author of Good Thinking: Seven Powerful Ideas That Influence the Way We Think.

Denise Dellarosa Cummins, Ph.D., is the author Good Thinking, The Historical Foundations of Cognitive Science, and Evolution of Mind.

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