The evolution of trust as a cognitive shortcut in repeated interactions

TL;DR

Trust and cooperation are intertwined in social interactions, but existing models confounded trust with cooperative outcomes. The authors formalize trust as a cognitive shortcut that reduces costly verification in repeated games and analyze trust-based strategies across the full space of symmetric two-player social dilemmas using evolutionary game theory. They show that trust-based strategies can outcompete Tit-for-Tat when verification is costly and errors occur, and that trust generally increases population-level cooperation, especially under high temptation to defect. The work provides a formal, observable measure of trust applicable to humans and AI, with implications for AI alignment and auditing regimes.

Abstract

Trust is often thought to increase cooperation. However, game-theoretic models often fail to distinguish between cooperative behaviour and trust. This makes it difficult to measure trust and determine its effect in different social dilemmas. We address this here by formalising trust as a cognitive shortcut in repeated games. This functions by avoiding checking a partner's actions once a threshold level of cooperativeness has been observed. We consider trust-based strategies that implement this heuristic, and systematically analyse their evolution across the space of two-player symmetric social dilemma games. We find that where it is costly to check whether another agent's actions were cooperative, as is the case in many real-world settings, then trust-based strategies can outcompete standard reciprocal strategies such as Tit-for-Tat in many social dilemmas. Moreover, the presence of trust increases the overall level of cooperation in the population, especially in cases where agents can make unintentional errors in their actions. This occurs even in the presence of strategies designed to build and then exploit trust. Overall, our results demonstrate the individual adaptive benefit to an agent of using a trust heuristic, and provide a formal theory for how trust can promote cooperation in different types of social interaction. We discuss the implications of this for interactions between humans and artificial intelligence agents.

Figures (7)

• Figure 1: Trust-based Cooperation (TUC) can be more robust to errors than Tit-for-Tat (TFT). The top panel shows a TUC agent playing against a TFT agent. Both agents start cooperating, and the trust threshold is reached by TUC. After a period of time, TFT makes an error and defects by mistake. However, because TUC has not verified its co-player's action on this round, this error is overlooked and mutual cooperation resumes for a number of rounds. At a later stage, TFT defects by mistake again. This time, TUC does verify, and reverts to playing TFT for the remaining rounds. By contrast, the lower pane shows that when TFT plays against itself, the first error always causes the breakdown of mutual cooperation.
• Figure 2: Frequency of the Tit-for-Tat (TFT) strategy (left), and the impact on the frequency of cooperation of adding TFT to the pool of available strategies AllC and AllD(right). The results are shown as a function of temptation to defect $T$ and sucker's payoff $S$, and in the absence ($\epsilon=0$, top panels) or presence ($\epsilon=0.25$, bottom panels) of an opportunity cost of verifying the partner's actions. Prisoner's Dilemma (PD) games occur in the lower right quadrant of $S$-$T$ space, Snowdrift (SD) games occur in the top right quadrant and Stag-Hunt (SH) games in the lower left quadrant. The red dots show the particular game instances that we use for later analysis. Parameters: a game with $r = 50$, and evolutionary dynamics with $\beta = 0.1$ and $N = 100$.
• Figure 3: Frequency of cooperators using the Tit-for-Tat strategy, in the absence of the opportunity cost of verifying the partner's actions (top), and with the cost $\epsilon=0.25$ (bottom). Parameters: a game with $r = 50$, and evolutionary dynamics where $\beta = 0.1$ and $N = 100$.
• Figure 4: Left: Frequency of strategies as a function of the opportunity cost, $\epsilon$. Right: Frequency of cooperation in the absence or presence of trust-based strategies TUC and TUD, as a function of the opportunity cost, $\epsilon$. The difference in frequency of cooperation when trust-based strategies are included is shaded in green where positive and red where negative. Results are presented for one example of each of the Prisoner's Dilemma, Snowdrift and Stag-Hunt games. Parameters: trust-based strategies with $\theta = 3$ and $p = 0.25$, games with $r = 50$, and evolutionary dynamics where $\beta = 0.1$ and $N = 100$.
• Figure 5: Frequency of the TUC strategy (left) and the impact of considering trust strategies on the frequency of cooperation (right), as a function of the temptation to defect $T$ and the sucker's payoff $S$. The difference in frequency of cooperation is calculated between a system with all five strategies and a system with only AllC, AllD and TFT. The red dots correspond to the values of S and T used in Figure \ref{['fig:epsilon']}. Parameters: trust-based strategies with $\theta = 3$ and $p = 0.25$, games with $\epsilon = 0.25$ and $r = 50$, and evolutionary dynamics with $\beta = 0.1$ and $N = 100$.