Fig. 6.

Mean squared error of the actual distribution of play relative to the best-response payoff, when matched with a partner playing the human distribution for possible preferences indexed by b. The average is across all games. The errors are plotted for each possible b, the weight on own vs partner payoff in the utility function. b = 1 is the purely selfish (own) payoff, b = 0 is the purely selfless/altruistic (partner) payoff, and b = 0.5 is the overall welfare (average) payoff, and other bs are weighted averages of own and partner payoffs. Both chatbots’ behaviors are best predicted by b = 0.5, and those of humans are best predicted by b = 0.6; they best predict ChatGPT-4’s behavior and have higher errors in the other cases. (A) The Top panel is for $\text{utility}=b\times \text{Own Payoff}+(1-b)\times \text{Partner Payoff}$. (B) The Bottom panel is for CES preferences: $\text{utility}={\left(b\times {(\text{Own Payoff})}^{1/2}+(1-b)\times {(\text{Partner Payoff})}^{1/2}\right)}^2$.