Benchmarking the efficacy of team decisions using a game theoretic approach

Abstract

In a consensus team decision-making process involving the allocation of resources, decision-makers arrive at a mutually beneficial and satisfying solution or strategy by unanimous agreement. However, this consensus agreement is often masked by behind-the-scene manoeuvres involving the consensus (or coalition) of subgroups, which then exert their influence (or threats) to advance the total team towards the masked consensus decision the subgroups had sought to institute. Finding the actual roles and motivations of parties in these behind-the-scene manoeuvres is difficult. However, the question we seek to answer is as follows: was it a true consensus decision that was arrived at? We answer the question by developing algebraic models of the decision-making problem within a game theoretic framework, for n decision-makers and m (pure) strategies involving resource apportioning. Using the Nash equilibrium as the basis for the coalition of subgroups, we identify the continuum cases of ‘win-win’, ‘win-lose’, ‘lose-win’ and ‘lose-lose’ decision outcomes. By means of a real-life case example, we then propose and apply this continuum of decision outcomes and their properties of regret, strategy selections and defining player subgroups, as standard benchmarks to assess the efficacy of the actual consensus team decision.

Keywords:

• benchmarking
• resource allocation
• consensus
• team decision-making
• Nash equilibrium
• game theory
• regret minimisation
• ‘win-win’