The Evolution of Lying in a Spatially-Explicit Prisoner's Dilemma Model

TL;DR

This study addresses how lying and honesty can evolve in a spatial Prisoner's Dilemma when agents may truthfully or deceitfully report their previous actions. It uses a 40×40 toroidal lattice where agents choose TFT or default strategies and possess a mutable truth-telling probability $P_{truth}$, evolving via mutation with reproduction biased by payoff. The key findings reveal two stable end-states—truth-telling cooperators and lying defectors—and identify a critical threshold around $P_{truth}=0.75$ that governs whether a mixed population evolves toward cooperation or defection; invasibility analyses further show that lying defectors are highly invasive and can destabilize cooperative states. These results offer insight into how signaling honesty and deception can shape the stability of cooperative behavior in social and biological systems, with implications for understanding political, ecological, and interspecies interactions that involve communication of intent.

Abstract

I present the results from a spatial model of the prisoner's dilemma, played on a toroidal lattice. Each individual has a default strategy of either cooperating ($C$) or defecting ($D$). Two strategies were tested, including ``tit-for-tat'' (TFT), in which individuals play their opponent's last play, or simply playing their default play. Each individual also has a probability of telling the truth ($0 \leq P_{truth} \leq 1$) about their last play. This parameter, which can evolve over time, allows individuals to be, for instance, a defector but present as a cooperator regarding their last play. This leads to interesting dynamics where mixed populations of defectors and cooperators with $P_{truth} \geq 0.75$ move toward populations of truth-telling cooperators. Likewise, mixed populations with $P_{truth} < 0.7$ become populations of lying defectors. Both such populations are stable because they each have higher average scores than populations with intermediate values of $P_{truth}$. Applications of this model are discussed with regards to both humans and animals.

Figures (11)

• Figure 1: Payoffs to the target in the prisoner's dilemma game used in this paper. Letters represent cooperators (C) and defectors (D) with the subscript representing the opponent. Note that regardless of what the opponent plays, the target receives a higher payout by defecting.
• Figure 2: Sample simulations over time for three different conditions, including playing tit-for-tat (TFT) with an initial probability of truth-telling ($IPT$) of 1.0 (row 1), TFT with $IPT = 0.0$ (row 2), and individuals playing their default strategies (row 3). Note that cooperators are blue (initially lower half of lattice) and defectors are red. For the TFT simulations, $P_{truth}$ was allowed to evolve. For the default strategy there is no querying of opponents so $P_{truth}$ does not play a role in those interactions. For this visualization, simulations were run on 50 x 50 toroidal lattice.
• Figure 3: The mean score (left) and mean $P_{truth}$ (right) at the end of simulations that ran for 1000 time steps on a 40 x 40 lattice. Only simulations with mutation = 0.1 (evolution) are included. For the default strategy scores (left graph), the communities end as either all cooperators or all defectors, leading individuals to having scores of either 24 or 8, respectively. When relying on their default strategy, the $P_{truth}$ follows a random walk (right graph, and see figure \ref{['randTP-time.fig']}). Note that in the mean $P_{truth}$ graph (right panel) the random initial setup, with individuals playing TFT, had an average less than 0.5 because runs that start with $IPT$ values less than 0.7 decay toward zero (see lower-left panel of figure \ref{['Truth.TFT']}). Error bars are 95% confidence intervals.
• Figure 4: Mean scores over time for simulations where $P_{truth}$ does (left panels) and does not (right panels) evolve. All individuals play the tit-for-tat strategy and start with all cooperators (row 1), all defectors (row 2), and a random distribution of cooperators and defectors (row 3). Note that the x-axis scale is logged.
• Figure 5: The mean $P_{truth}$ over time for simulations for which $P_{truth}$ does (left panels) and does not (right panels) evolve. Initial $P_{truth}$ ($IPT$) values range from 0 to 1, by 0.025. All individuals use the tit-for-tat strategy and start with all cooperators (row 1), all defectors (row 2), and a random distribution of cooperators and defectors (row 3). $P_{truth}$ values in the left panels do not end at either 0.0 or 1.0 exactly due to mutation. Note that the x-axis scales are logged.