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Modelling the Dynamics of Identity and Fairness in Ultimatum Game

Janvi Chhabra, Jayati Deshmukh, Arpitha Malavalli, Karthik Sama, Srinath Srinivasa

TL;DR

This paper tackles how subjective identity interacts with fairness in allocation, using a Computational Transcendence framework to model elastic identity in autonomous agents. It extends CT by embedding a fairness threshold and examining the Ultimatum Game, deriving two fairness representations: a fixed agent-based threshold and an association-based threshold that ties fairness to semantic distance and identity. Key contributions include formalizing perceived payoff via a sigmoid loss function, proposing a dual-stage utility computation, and demonstrating how dynamic thresholds produce more varied and potentially fairer allocation outcomes compared to baseline identity-only models. The work offers a principled approach to incorporating human-like notions of fairness into autonomous agents, with implications for resource-sharing in multi-agent systems and human-agent interaction contexts.

Abstract

Allocation games are zero-sum games that model the distribution of resources among multiple agents. In this paper, we explore the interplay between an \textit{subjective identity} and its impact on notions of fairness in allocation. The sense of identity in agents is known to lead to responsible decision-making in non-cooperative, non-zero-sum games like Prisoners' Dilemma, and is a desirable feature to add into agent models. However, when it comes to allocation, the sense of identity can be shown to exacerbate inequities in allocation, giving no rational incentive for agents to act fairly towards one another. This lead us to introduce a sense of fairness as an innate characteristic of autonomous agency. For this, we implement the well-known Ultimatum Game between two agents, where their sense of identity association and their sense of fairness are both varied. We study the points at which agents find it no longer rational to identify with the other agent, and uphold their sense of fairness, and vice versa. Such a study also helps us discern the subtle difference between responsibility and fairness when it comes to autonomous agency.

Modelling the Dynamics of Identity and Fairness in Ultimatum Game

TL;DR

This paper tackles how subjective identity interacts with fairness in allocation, using a Computational Transcendence framework to model elastic identity in autonomous agents. It extends CT by embedding a fairness threshold and examining the Ultimatum Game, deriving two fairness representations: a fixed agent-based threshold and an association-based threshold that ties fairness to semantic distance and identity. Key contributions include formalizing perceived payoff via a sigmoid loss function, proposing a dual-stage utility computation, and demonstrating how dynamic thresholds produce more varied and potentially fairer allocation outcomes compared to baseline identity-only models. The work offers a principled approach to incorporating human-like notions of fairness into autonomous agents, with implications for resource-sharing in multi-agent systems and human-agent interaction contexts.

Abstract

Allocation games are zero-sum games that model the distribution of resources among multiple agents. In this paper, we explore the interplay between an \textit{subjective identity} and its impact on notions of fairness in allocation. The sense of identity in agents is known to lead to responsible decision-making in non-cooperative, non-zero-sum games like Prisoners' Dilemma, and is a desirable feature to add into agent models. However, when it comes to allocation, the sense of identity can be shown to exacerbate inequities in allocation, giving no rational incentive for agents to act fairly towards one another. This lead us to introduce a sense of fairness as an innate characteristic of autonomous agency. For this, we implement the well-known Ultimatum Game between two agents, where their sense of identity association and their sense of fairness are both varied. We study the points at which agents find it no longer rational to identify with the other agent, and uphold their sense of fairness, and vice versa. Such a study also helps us discern the subtle difference between responsibility and fairness when it comes to autonomous agency.
Paper Structure (21 sections, 4 equations, 9 figures)

This paper contains 21 sections, 4 equations, 9 figures.

Table of Contents

  1. Introduction
  2. Related Work
  3. Ultimatum Game
  4. UG in Humans
  5. Modelling Fairness in UG
  6. Inequity Aversion based Model
  7. Reciprocity based Model
  8. Emotion and Cognition based Model
  9. Social Decision-Making in Ultimatum Game
  10. Computational Transcendence
  11. Baseline Model
  12. Notion of Fairness
  13. Perceived Payoff
  14. Utility Computation
  15. Agent-based Fairness Threshold
  16. ...and 6 more sections

Figures (9)

  • Figure 1: The Ultimatum Game
  • Figure 2: Utility of a transcended agent for possible splits for various $\gamma$ values. The blue circles are Maximum Utility Split and the red circles are Minimum Acceptable Utility
  • Figure 3: Perceived Payoff Function
  • Figure 4: The utility curve of the transcended agents ($\gamma$ = 0.5, $\tau$ = 0.5) w.r.t possible splits while varying the semantic distance of the agent with another player
  • Figure 5: Utility curves with different combination for extremes values of $\tau$ and $\gamma$
  • ...and 4 more figures