Emergence of heterogeneity in a noncompetitive resource allocation problem

Area of Science:

• Game theory
• Agent-based modeling
• Thermodynamics

Background:

• Simultaneously adjusting shower temperatures in hotels creates complex coordination problems.
• Imperfect information and increasing temperature sensitivity with more users make optimal temperature control difficult.
• Finite tap positions limit the ability of identical agents to achieve desired temperatures.

Purpose of the Study:

• To analyze the challenges of temperature control in shared hotel shower systems.
• To investigate the stability of homogeneous strategies in a multi-agent system.
• To explore the emergence of strategy heterogeneity.

Main Methods:

• Modeling the shower tuning process as a game theory problem.
• Analyzing agent interactions under conditions of imperfect information.
• Employing evolutionary stability theory to assess strategy populations.

Main Results:

• Homogeneous strategies within a population are shown to be evolutionarily unstable.
• The number of agents significantly impacts temperature sensitivity and learnability.
• Identical agents struggle to reach preferred temperatures due to finite control positions.

Conclusions:

• Heterogeneity in agent strategies is a likely outcome in such systems.
• While heterogeneity may seem beneficial, it carries inherent risks.
• Understanding these dynamics is crucial for designing more effective control systems.