We investigate the relationship between the team-optimal solution and the Nash equilibrium (NE) to assess the impact of strategy deviation on team performance. As a working use case, we focus on a class of flow assignment problems in which each source node acts as a cooperating decision maker (DM) within a team that minimizes the team cost based on the team-optimal strategy. In practice, some selfish DMs may prioritize their own marginal cost and deviate from NE strategies, thus potentially degrading the overall performance. To quantify this deviation, we explore the deviation bound between the team-optimal solution and the NE in two specific scenarios: (i) when the team-optimal solution is unique and (ii) when multiple solutions do exist. This helps DMs analyze the factors influencing the deviation and adopting the NE strategy within a tolerable range. Furthermore, in the special case of a potential game model, we establish the consistency between the team-optimal solution and the NE. Once the consistency condition is satisfied, the strategy deviation does not alter the total cost, and DMs do not face a strategic trade-off. Finally, we validate our theoretical analysis through some simulation studies.

翻译：本研究旨在探讨团队最优解与纳什均衡（NE）之间的关系，以评估策略偏离对团队绩效的影响。作为一个具体研究案例，我们聚焦于一类流量分配问题，其中每个源节点作为团队中的合作决策者（DM），基于团队最优策略最小化团队成本。实践中，部分自私的DM可能优先考虑自身边际成本并偏离NE策略，从而可能导致整体性能下降。为量化这种偏离，我们在两种特定场景下探究团队最优解与NE之间的偏离界限：（i）当团队最优解唯一时；（ii）当存在多个解时。这有助于DM分析影响偏离的因素，并在可容忍范围内采用NE策略。此外，在势博弈模型这一特殊情形中，我们建立了团队最优解与NE之间的一致性条件。一旦满足该一致性条件，策略偏离将不会改变总成本，且DM无需面临策略权衡。最后，我们通过仿真研究验证了理论分析结果。