INFLUENCE OF PROMPT FRAMING ON LLM STRATEGIC BEHAVIOUR IN CLASSICAL GAMES

Abstract

This article addresses whether strategic choices of LLM in classical games can be manipulated solely by changing the wording of the system prompt (framing), with the payoff structure held constant. The issue has both scientific and practical relevance: if LLM behaviour can be substantially altered by editing the prompt without changing the rules of the game, there is a risk of manipulation and potential fraud, where one party may tailor prompts to induce behaviour favourable to itself. The study aims to test this hypothesis empirically in four canonical games - the Prisoner’s Dilemma, Stag Hunt, Public Goods Game, and Ultimatum Game - under four prompt conditions: control (rational payoff maximization), cooperative, competitive, and ethical.

The experimental design involved matches in an LLM-versus-LLM format with the same prompt condition for both players. For each game–condition combination, a series of matches with multiple rounds was run. Results show a clear dependence of behaviour on framing: under the cooperative condition, full cooperation is observed in the Prisoner’s Dilemma and Stag Hunt, a high average contribution in the Public Goods, and the highest offers in the Ultimatum Game. Under control and competitive framing, cooperation in the first two games is minimal or zero, contribution in the Public Goods Game is effectively zero, and Ultimatum offers are lowest. The ethical condition yields intermediate outcomes.

The findings support that prompt framing is substantially associated with changes in strategic behaviour across all four games with unchanged payoffs. This is directly relevant to identifying manipulation risks when deploying LLM in negotiations, bargaining, and multi-agent systems, and to further study of replication and generalization to other models and interaction scenarios.