Pigeons (Columba livia) approach Nash equilibrium in experimental Matching Pennies competitions.
Pigeons deviate from optimal random play in competitive games the same way humans do, and a plain learning rule predicts it.
01Research in Context
What this study did
Federico and colleagues put pigeons in a two-player game called Matching Pennies.
Each trial the bird pecked left or right.
A computer opponent also picked left or right.
If the choices matched, the pigeon earned grain.
If they mismatched, no grain.
The payoff matrix was shown on colored cards so the bird always knew the rules.
Sessions ran until choice patterns stabilized.
What they found
The birds did not play the perfect random strategy game theory says is best.
They drifted into predictable patterns that looked a lot like human data.
A simple linear learning model—just update choice strength after each win or loss—fit the deviations well.
No fancy mind-reading math was needed.
How this fits with other research
Older pigeon work on concurrent schedules already showed birds often follow the matching law, not strict maximization.
Macdonald et al. (1973) found response ratios matched reinforcement ratios on VI-VI schedules.
Yuwiler et al. (1992) saw the same on time-based schedules.
Those studies used independent concurrent keys, while Federico used a competitive game where the opponent fights back.
The new twist is that even with signaled payoffs the birds still deviate from Nash equilibrium, echoing the earlier non-maximizing results.
Spanoudis et al. (2011) later showed pigeons rapidly shift choice criteria when payoffs change, confirming that small contingency tweaks produce quick, orderly drift—supporting the linear learning idea Federico used.
Why it matters
If pigeons—and people—depart from optimal play in the same simple way, you can skip complex cognitive models.
Use a basic learning rule plus feedback to predict and shape choice.
In the clinic, when clients face competitive or probabilistic tasks, expect systematic drift rather than perfect adjustment.
Reinforce small steps toward better randomization and track the pattern with a linear model.
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02At a glance
03Original abstract
The game of Matching Pennies (MP), a simplified version of the more popular Rock, Papers, Scissors, schematically represents competitions between organisms with incentives to predict each other's behavior. Optimal performance in iterated MP competitions involves the production of random choice patterns and the detection of nonrandomness in the opponent's choices. The purpose of this study was to replicate systematic deviations from optimal choice observed in humans when playing MP, and to establish whether suboptimal performance was better described by a modified linear learning model or by a more cognitively sophisticated reinforcement-tracking model. Two pairs of pigeons played iterated MP competitions; payoffs for successful choices (e.g., "Rock" vs. "Scissors") varied within experimental sessions and across experimental conditions, and were signaled by visual stimuli. Pigeons' behavior adjusted to payoff matrices; divergences from optimal play were analogous to those usually demonstrated by humans, except for the tendency of pigeons to persist on prior choices. Suboptimal play was well characterized by a linear learning model of the kind widely used to describe human performance. This linear learning model may thus serve as default account of competitive performance against which the imputation of cognitively sophisticated processes can be evaluated.
Journal of the experimental analysis of behavior, 2009 · doi:10.1901/jeab.2009.91-169