Responses to a simple barter task in chimpanzees, Pan troglodytes

Abstract

Chimpanzees (Pan troglodytes) frequently participate in social exchange involving multiple goods and services of variable value, yet they have not been tested in a formalized situation to see whether they can barter using multiple tokens and rewards. We set up a simple barter economy with two tokens and two associated rewards and tested chimpanzees on their ability to obtain rewards by returning the matching token in situations in which their access to tokens was unlimited or limited. Chimpanzees easily learned to associate value with the tokens, as expected, and did barter, but followed a simple strategy of favoring the higher-value token, regardless of the reward proffered, instead of a more complex but more effective strategy of returning the token that matched the reward. This response is similar to that shown by capuchin monkeys in our previous study. We speculate that this response, while not ideal, may be sufficient to allow for stability of the social exchange system in these primates, and that the importance of social barter to both species may have led to this convergence of strategies.

Appendix 1: Calculations for determining expected frequency of reward returns

There are twenty ways to randomly arrange three high-value rewards and three low-value rewards in a series of six trials. These can be divided into four basic classes.

• Three high-value rewards followed by three low-value rewards (one possibility)

• Two high-value rewards and one low-value reward in the first three trials, followed by one high-value reward and two low value rewards in the second three trials (nine possibilities)

• One high-value reward and two low-value rewards in the first three trials, followed by two high-value rewards and one low-value reward in the second three trials (nine possibilities)

• Three low-value rewards followed by three high-value rewards (one possibility)

If the arrangements of the trials is truly random, each possibility is equally likely, making it nine times more likely that a series will fall into the second or third class than into the first or fourth. By calculating the return generated by a particular strategy in each class of trial, multiplying those returns by the probability of encountering each class, and adding the products, we can calculate the expected return of that strategy under these conditions.

An individual pursuing the matching strategy will receive three high-value rewards and three low-value rewards from any of these trials, yielding an expected return of three high-value rewards and three low value rewards.

$$ \begin{aligned} E({\text{reward}}) & = \frac{1} {{20}}\left( {3H + 3L} \right) + \frac{9} {{20}}\left( {3H + 3L} \right) + \frac{9} {{20}}\left( {3H + 3L} \right)\frac{1} {{20}}\left( {3H + 3L} \right) \\ E\,({\text{reward}}) & = 3H + 3L \\ \end{aligned} $$

An individual pursuing the high value strategy with limited tokens will return the high-value tokens followed by the low-value tokens, with a total return ranging from three high-value rewards and three low-value rewards to no reward at all. The expected return is 1.5 high-value rewards and 1.5 low-value rewards.

$$ \begin{aligned} E\,({\text{reward}}) & = \frac{1} {{20}}\left( {3H + 3L} \right) + \frac{9} {{20}}\left( {2H + 2L} \right) + \frac{9} {{20}}\left( {1H + 1L} \right)\frac{1} {{20}}\left( {0H + 0L} \right) \\ E\,({\text{reward}}) & = \frac{1} {{20}}\left( {3H + 3L + 18H + 18L + 9H + 9L} \right) = \frac{1} {{20}}(30H + 30L) \\ E\,({\text{reward)}} & = \frac{3} {2}H + \frac{3} {2}L \\ \end{aligned} $$

An individual pursuing the high value strategy with unlimited tokens will return high-value tokens for every trial. The expected return is three high-value rewards.

$$ \begin{aligned} E\,({\text{reward}}) & = \frac{1} {{20}}\left( {3H + 0L} \right) + \frac{9} {{20}}\left( {3H + 0L} \right) + \frac{9} {{20}}\left( {3H + 0L} \right)\frac{1} {{20}}\left( {3H + 0L} \right) \\ E\,({\text{reward}}) & = \frac{1} {{20}}\left( {3H + 27H + 27H + 3H} \right) = \frac{{60}} {{20}}H \\ E\,({\text{reward}}) & = 3H \\ \end{aligned} $$

An individual pursuing random strategy will return tokens with no regard to their value. For any given series of trials with limited tokens, there is a 1/20 chance that the individual will match the trials perfectly, a 9/20 chance that the individual will miss one low-value and one high-value reward, a 9/20 chance that the individual will miss two low-value and two high-value rewards, and a 1/20 chance that the individual will not match any trials correctly. The results are restricted to these four combinations (3 and 3, 2 and 2, 1 and 1, 0 and 0) because of the token-limited nature of the trials. The expected return is 1.5 high-value rewards and 1.5 low value rewards, using calculations similar to those in the token-limited maximum value strategy.

An individual pursuing the random strategy in a series of trials with freely available tokens has a 1/2 chance of earning a reward on each trial. This arrangement provides a much wider spectrum of possible reward combinations than does the token-limited situation, as the numbers of high-value and low-value rewards are no longer constrained to be equal, but the expected return does not change.

$$ \begin{aligned} E\,({\text{reward}}) & = 3 \times \frac{1} {2}H + 3 \times \frac{1} {2}L \\ E\,({\text{reward}}) & = \frac{3} {2}H + \frac{3} {2}L \\ \end{aligned} $$