A Computational Analysis of Strategic Nominations: Modeling Equilibrium and Complexity in Organizational Elections

This paper models organizational electoral competition as an election game with strategic organizations in a macro level. Members of the organization derive utility from the elected candidate. Each organization nominates exactly one candidate to compete against candidates from other organizations and the payoff of each organization is the expected utility its members receive. By simulating the voting outcomes in the competitions between two and three organizations, we reveal and validate the monotone correspondence between the utility received by the voters and the chance of winning in the competition. Next, we show that pure-strategy Nash equilibria (PSNE) do not always exist for the election games with three or more groups, even under egoistic conditions, and prove that determining the PSNE existence is {\sf NP}-complete in general-form representation. Addressing this, we propose sufficient conditions for PSNE existence and develop a fixed-parameter tractable algorithm to compute equilibria, parameterized by irresolute groups and nominating depth. We also show that the price of anarchy for egoistic election games is upper bounded by the number of competing groups. These findings highlight how stability and efficiency can deteriorate with increased group participation, offering computational insights into multi-group strategic decision-making.