Iterated crowdsourcing dilemma game

The Internet has enabled the emergence of collective problem solving, also known as crowdsourcing, as a viable option for solving complex tasks. However, the openness of crowdsourcing presents a challenge because solutions obtained by it can be sabotaged, stolen, and manipulated at a low cost for the attacker. We extend a previously proposed crowdsourcing dilemma game to an iterated game to address this question. We enumerate pure evolutionarily stable strategies within the class of so-called reactive strategies, i.e., those depending on the last action of the opponent. Among the 4096 possible reactive strategies, we find 16 strategies each of which is stable in some parameter regions. Repeated encounters of the players can improve social welfare when the damage inflicted by an attack and the cost of attack are both small. Under the current framework, repeated interactions do not really ameliorate the crowdsourcing dilemma in a majority of the parameter space.

💡 Research Summary

The paper investigates whether repeated interactions can mitigate the “crowdsourcing dilemma,” a situation where two competing firms may choose to outsource problem solving to a crowd (crowdsourcing) but also have the option to sabotage the opponent’s crowdsourced solution at a low cost. Building on a previously proposed two‑stage, one‑shot crowdsourcing dilemma game, the authors formulate an iterated version in which each round consists of a decision to crowdsource or not and, conditional on the opponent’s choice, a decision to attack or not. The key novelty is that both decisions are made simultaneously without knowledge of the opponent’s productivity, and each decision is subject to a small implementation error ε.

In the iterated setting the authors restrict attention to “reactive strategies,” i.e., strategies that condition the current action solely on the opponent’s realized action in the previous round. Since there are four possible actions (CA, CN, SA, SN) and six possible realized outcomes (CA, CN, C*, SA, SN, S*), the total number of reactive strategies is 4⁶ = 4096. Using exhaustive enumeration and evolutionary stability analysis, they identify 16 strategies that are Evolutionarily Stable Strategies (ESSs) in some region of the parameter space defined by the damage inflicted by an attack (d ∈ (0,1)) and the cost of launching an attack (q ∈ (0,1)).

The non‑iterated game reproduces the three classic regimes known from the original model: (i) both firms crowdsource when d is low or q is high, (ii) both firms solve in‑house (no crowdsourcing) when d is high and q is low, and (iii) coexistence of the two pure equilibria when both d and q are high. In the iterated game, three of the 16 ESSs are unconditional (always choose CA, CN, or SA), while the remaining 13 are conditional strategies that respond to the opponent’s last realized action. Notably, two conditional strategies—labeled 12 and 14 in the paper—are efficient (i.e., yield higher average payoffs) in the region where both d and q are small (region A). Strategy 12 essentially plays “crowdsource‑and‑attack unless the opponent just attacked,” whereas strategy 14 adopts a “tit‑for‑tat‑like” rule: it attacks only after the opponent has attacked in the previous round.

Efficiency is assessed by computing the stationary average payoff of a homogeneous population using each ESS. In regions B and C (moderate d, low q or high q), the unconditional strategies CN and SA remain the most efficient, matching the one‑shot results. In region A, the conditional strategies 12 and 14 outperform the unconditional “always crowdsource and attack” (uncond‑CA) because the presence of implementation errors (ε) creates occasional periods where both players refrain from attacking (SA), thereby saving the attack cost q. The payoff advantage of strategy 14 over uncond‑CA persists even as ε → 0, because strategy 14 can sustain a long run of SA states when paired with an opponent using uncond‑CA, whereas uncond‑CA inevitably incurs the attack cost each round.

The authors also examine the size of the attractive basins under replicator dynamics (restricted to the identified ESSs) to gauge evolutionary plausibility. For ε = 10⁻³, the basins of strategies 12 and 14 are larger than that of uncond‑CA across most of region A, indicating that these conditional strategies can dominate from a wide range of initial conditions.

Overall, the study finds that repeated encounters improve social welfare only when both the damage from attacks and the cost of attacks are low; in the majority of the (d, q) space, iterating the game does not alleviate the crowdsourcing dilemma. The work highlights that simply allowing repeated interactions is insufficient to foster cooperation in crowdsourcing competitions; rather, the structure of strategies (especially conditional retaliation) and the presence of small execution errors are crucial for the emergence of mutually beneficial outcomes. The authors suggest that future extensions could incorporate longer memory strategies, multi‑player settings, or institutional mechanisms such as reputation systems to further explore pathways toward cooperation in crowdsourced environments.