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The evolution of trust and trustworthiness

Aanjaneya Kumar, Valerio Capraro, Matjaz Perc

arXiv:2008.12948v1physics.soc-phcs.SIq-bio.PE

TL;DR

The paper asks how trust and trustworthiness can evolve despite their costs and whether network structure helps. It models them with the trust game across well-mixed and networked populations, finding little effect of structure in most cases and joint evolution only in a limited scale-free, unnormalized-dynamics case.

  • Problem

    Because prosocial behavior can require giving up personal benefits, the paper asks whether network reciprocity promotes trust and trustworthiness as it has promoted other behaviors.

    Source: §I · pp. 1–2

  • Method

    The authors simulate a binary trust game across well-mixed and networked populations, comparing normalized and unnormalized imitation dynamics on heterogeneous networks.

    Source: B. The Monte Carlo method · p. 3, §IV · p. 6

  • Results

    Trust rarely evolves across the studied settings; both trust and trustworthiness evolve with non-negligible probability only in a small region of scale-free networks under unnormalized dynamics.

    Source: §IV · pp. 6–7

  • Takeaways & Limitations

    The observed prevalence of trust and trustworthiness leaves open which mechanisms promote them, with good samaritans and noisy imitation raised as directions for further study.

    Source: §IV · p. 7

    The study operationalizes trust and trustworthiness through a binary version of the trust game.

    Source: §IV · p. 6

Abstract

from arXiv · show

Trust and trustworthiness form the basis for continued social and economic interactions, and they are also fundamental for cooperation, fairness, honesty, and indeed for many other forms of prosocial and moral behavior. However, trust entails risks, and building a trustworthy reputation requires effort. So how did trust and trustworthiness evolve, and under which conditions do they thrive? To find answers, we operationalize trust and trustworthiness using the trust game with the trustor's investment and the trustee's return of the investment as the two key parameters. We study this game on different networks, including the complete network, random and scale-free networks, and in the well-mixed limit. We show that in all but one case the network structure has little effect on the evolution of trust and trustworthiness. Specifically, for well-mixed populations, lattices, random and scale-free networks, we find that trust never evolves, while trustworthiness evolves with some probability depending on the game parameters and the updating dynamics. Only for the scale-free network with degree non-normalized dynamics, we find parameter values for which trust evolves but trustworthiness does not, as well as values for which both trust and trustworthiness evolve. We conclude with a discussion about mechanisms that could lead to the evolution of trust and outline directions for future work.

I. INTRODUCTION

Trust and trustworthiness are prosocial behaviors that challenge narrow self-interest, and the paper asks whether network structure can promote their evolution. It applies evolutionary-game methods to the trust game, extending prior work on other forms of prosocial and moral behavior.

I. INTRODUCTION

  • Prosocial behavior can require giving up personal benefits, so the authors frame the evolution of mechanisms favoring it as a major research challenge.The introduction situates this question across sociology, psychology, anthropology, economics, biology, and physics.Source: §I · p. 1
  • The paper situates its approach in network science and statistical physics, where Monte Carlo simulations have been used to study prosocial behavior on networks.Earlier work focused especially on cooperation, strategic fairness, and altruistic punishment.Source: §I · p. 1
  • The paper applies methods used to study cooperation and altruistic punishment to the evolution of trust and trustworthiness, following work on truth-telling.Recent empirical research treats cooperation and altruistic punishment as forms of moral behavior, motivating this extension.Source: §I · p. 1
  • Trust involves a trustor accepting vulnerability in hope of a return from a trustee, even though the trustee may keep the gains.The passage links trust and trustworthiness to cooperation and altruism and describes returning favors as a moral rule found across 60 societies [58].Source: §I · p. 1
  • Network reciprocity has promoted cooperation and, in some cases, fairness, altruistic punishment, and truth-telling; the paper asks whether it also promotes trust and trustworthiness.The authors motivate this question by noting that real interactions are structured and that trust and trustworthiness are observed despite conflicting with narrow self-interest.Source: §I · p. 2

A. The trust game

The trust game measures trust through a trustor’s investment and trustworthiness through a trustee’s return. Although backward induction predicts no trust or return in a one-shot anonymous game, experiments report both behaviors.

A. The trust game

  • The trustor transfers a share x of an endowment to the trustee; the trustee then returns a fraction r of the tripled transfer.The resulting payoffs are 1−x+3xr for the trustor and 3x(1−r) for the trustee.Source: A. The trust game · p. 2
  • In a one-shot anonymous game, backward induction predicts that the trustee returns nothing and the trustor does not trust.Experiments nevertheless report nonzero transfers and substantial returns, including among participants who understand payoff maximization and are not simply risk-seeking.Source: A. The trust game · p. 2
  • The authors argue that the trust game differs fundamentally from the prisoner’s dilemma, despite their superficial resemblance.The trust game is asymmetric, whereas the prisoner’s dilemma is symmetric, and the games generate different evolutionary patterns.Source: A. The trust game · p. 2

B. The Monte Carlo method

The simulations model a binary trust game and use Monte Carlo updates to estimate strategy frequencies in well-mixed and structured populations. For heterogeneous networks, they compare imitation rules that either account for player degree or do not.

B. The Monte Carlo method

  • The binary game assigns trust to the trustor’s choice and trustworthiness to the trustee’s choice, with parameters x and r describing the investment and return.The authors also single out x = 1 and r = 0.5 as the case where the trustor invests all her endowment and the return yields an equal split.Source: B. The Monte Carlo method · pp. 2–3
  • In well-mixed simulations, agents receive the four strategies at random, play with randomly chosen opponents, and one player may copy another’s strategy based on their payoffs.Each pair plays eight games with roles assigned randomly; the simulation repeats the update N times per full Monte Carlo step.Source: B. The Monte Carlo method · p. 3
  • Each realization can run for up to 10,000 full Monte Carlo steps, and reported evolution averages 5,000 realizations with randomized initial conditions.The imitation parameter is K = 0.1.Source: B. The Monte Carlo method · p. 3
  • On structured populations, players are restricted to neighbors; heterogeneous networks use normalized and unnormalized replicator dynamics.Normalized dynamics scale payoffs by player degree, while unnormalized dynamics do not; the two rules represent imitation with or without accounting for connection counts.Source: B. The Monte Carlo method · p. 3
  • The well-mixed results plot stationary densities of four strategies over a 20 × 20 grid of x and r values, each ranging from 0 to 1.The figure caption identifies the population as well-mixed.Source: Figure 1 · p. 3

A. Well-mixed populations

In well-mixed populations, trust disappears at steady state across the tested parameter values, while trustworthiness varies with the return parameter. A representative trajectory shows the non-trusting, non-reciprocating strategy dominating.

A. Well-mixed populations

  • Both trust strategies, (T,R) and (T,B), have zero steady-state density in well-mixed populations, irrespective of x and r.The result is reported for a population of 500 agents.Source: A. Well-mixed populations · p. 3
  • Trustworthiness is about 50% for very small r and decreases monotonically as r increases, with little dependence on x.This pattern is reported for each value of x.Source: A. Well-mixed populations · p. 3
  • For x = 1 and r = 0.5, the non-trusting, betraying strategy (N,B) survives at about 85%, while (N,R) accounts for about 15%.The trust strategies decline to zero after about 40 Monte Carlo steps.Source: A. Well-mixed populations · pp. 3–4

B. Lattices

Lattice structure has little effect on the strategy trends seen in well-mixed populations. Trust strategies disappear in the reported example, while a few realizations show long-lived coexistence between two non-trusting strategies.

B. Lattices

  • Lattice simulations preserve the well-mixed trends, with only small numerical differences across square, triangular, and hexagonal lattices.For x = 1 and r = 0.5, (T,R) and (T,B) quickly vanish; (N,R) is about 5% higher and (N,B) slightly lower than in well-mixed populations.Source: B. Lattices · p. 4
  • The reported late-time snapshots are selected from a 40 × 40 square-lattice run and represent a rare coexistence realization.The caption notes that most realizations instead enter an absorbing state.Source: Figure 3 · p. 4
  • Most square-lattice realizations reach a single-strategy absorbing state, but a few sustain long-lived (N,B) and (N,R) coexistence.The surviving strategies form metastable clusters and also appear in alternating patches; the figure shows one such realization.Source: B. Lattices · p. 4, Figure 3 · p. 4

C. Random and scale-free networks

Random networks resemble well-mixed populations and lattices, but scale-free networks behave differently under unnormalized dynamics: trust can evolve at low x, while normalized dynamics show no trust evolution.

C. Random and scale-free networks

  • The random and scale-free simulations used 500 agents and average degree close to 10; scale-free networks were generated with the Barabási–Albert algorithm.Both normalized and unnormalized replicator dynamics were considered because these networks are not regular.Source: C. Random and scale-free networks · p. 4
  • Random-network results closely match well-mixed populations and lattices under both normalized and unnormalized dynamics, providing evidence that spatial correlations alone do not produce trust.Source: C. Random and scale-free networks · p. 4
  • With normalized dynamics, trust does not evolve; with unnormalized dynamics, (T,R) evolves for small x and (T,B) for x < 0.5, reaching nearly 50% in an island.The scale-free results depend on the choice of replicator dynamics.Source: C. Random and scale-free networks · p. 5
  • At x=1 and r=0.5, normalized scale-free dynamics resemble the well-mixed case, while unnormalized dynamics allow (T,B) to persist at very low frequency.Source: C. Random and scale-free networks · p. 5, Figure 5 · p. 5
  • At x=0.1, r=0.8, (T,B) reaches close to 50% and (T,R) about 2%; at r=0.3, (T,R) reaches about 15% and (N,R) about 25%, versus 5% at r=0.8.These contrasting cases are shown for unnormalized replicator dynamics.Source: C. Random and scale-free networks · pp. 5–6, Figure 6 · p. 5

IV. DISCUSSION

Across the tested populations, trust and trustworthiness rarely evolve together; the exception is scale-free networks with unnormalized imitation, where outcomes depend on the game parameters. The discussion also considers how this narrow result compares with prior work and what other mechanisms might support trust.

IV. DISCUSSION

  • Trust rarely evolves across the tested populations; only scale-free networks with unnormalized dynamics yield joint trust and trustworthiness, around 15% for small x and r, while trust alone reaches around 50% for small x and large r.In well-mixed populations, trustworthiness instead decreases as r increases and depends little on x.Source: §IV · pp. 6–7
  • The authors distinguish the asymmetric trust game from the prisoner’s dilemma, where spatial structure generally favors cooperation but has little effect on trust.They describe this as the first systematic study of trust and trustworthiness evolution on networks.Source: §IV · p. 7
  • Adding one good samaritan who always plays (T,R) leaves a small fraction of trustors in the stationary state where trust previously did not evolve.The simulation tracks the other 499 agents in a well-mixed population of 500.Source: §IV · p. 7
  • At K=10, noisy imitation yields about 10% trust and about 1% (T,R) at steady state for x=1 and r=0.5.The paper interprets noise as imperfect payoff information or sub-optimal decision making.Source: §IV · p. 7
  • The results concern particular networks and imitation rules; the authors identify other structures, update rules, individual differences, reputation, and social responses as avenues for further study.They cite online transaction rating systems as an example of reputation mechanisms that could promote trust.Source: §IV · p. 7
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