Grounded Predictions of Teamwork as a One-Shot Game: A Multiagent Multi-Armed Bandits Approach

TL;DR

This study delves into the feasibility of collaboration within teams of rational, self-interested agents who engage in teamwork without the obligation to contribute, and characterises this novel game's Nash equilibria and proposes a multiagent multi-armed bandit system that learns to converge to approximations of such equilibria.

Abstract

Humans possess innate collaborative capacities. However, effective teamwork often remains challenging. This study delves into the feasibility of collaboration within teams of rational, self-interested agents who engage in teamwork without the obligation to contribute. Drawing from psychological and game theoretical frameworks, we formalise teamwork as a one-shot aggregative game, integrating insights from Steiner's theory of group productivity. We characterise this novel game's Nash equilibria and propose a multiagent multi-armed bandit system that learns to converge to approximations of such equilibria. Our research contributes value to the areas of game theory and multiagent systems, paving the way for a better understanding of voluntary collaborative dynamics. We examine how team heterogeneity, task typology, and assessment difficulty influence agents' strategies and resulting teamwork outcomes. Finally, we empirically study the behaviour of work teams under incentive systems that defy analytical treatment. Our agents demonstrate human-like behaviour patterns, corroborating findings from social psychology research.

Figures (9)

• Figure 1: Player $i$'s utility $\widetilde{u_i}(g_i, \sigma(G_{-i}))$, across three regime values of $G_{-i}$. Upper pannel: $G_{-i} > G_{-i}^{*}$. Middle pannel: $G_{-i} = G_{-i}^*$ . Bottom pannel: $G_{-i} < G_{-i}^*$. Adapted from cornes2007weak.
• Figure 2: Top panel: The teamwork outcome $G$, as given by Eq. (\ref{['eq:G_local_max']}), is depicted in two different shades of blue and has a bell shape. The boundary line of the left-hand inequality in Eq. (\ref{['ineq:best_response_correspondence']}), shown in fuchsia, intersects this graph at $(g_i^*, G_{i}^*)$. The boundary line of the right-hand inequality in Eq. (\ref{['ineq:best_response_correspondence']}), shown in light orange, is to the right of the fuchsia line and intersects the graph at $(\overline{g}_i, \overline{G}_i)$. The teamwork outcome $G$, as given by Eq. (\ref{['eq:G_local_max']}), is depicted in two different shades of blue and has a bell shape. The boundary line of the left-hand inequality in Eq. (\ref{['ineq:best_response_correspondence']}), shown in fuchsia, intersects this graph at $(g_i^*, G_{i}^*)$. The boundary line of the right-hand inequality in Eq. (\ref{['ineq:best_response_correspondence']}), shown in light orange, is to the right of the fuchsia line and intersects the graph at $(\overline{g}_i, \overline{G}_i)$. The non-shaded area indicates the region of $G$ that satisfies both the local and global maximum conditions simultaneously (bold blue segment). Bottom panel: Reflection of the teamwork outcome $G$ across the $45\degree$ line, showing only the region where $G$ meets the local and global maximum conditions. Figures adapted from cornes2007weak.
• Figure 3: The two components of player $i$'s share correspondence when $\frac{\rho}{\Delta_t p_i^{\mathcal{T}}}\geq \frac{\sigma^{\prime}(\overline{G}_i)}{\sigma (\overline{G}_i)}\frac{\beta_i^{1/\rho}}{\alpha}$
• Figure 4: Logistic evaluation function with passing threshold $b=3$, steepness parameter $\gamma = 2$, and right-hand asymptote $d=10$.
• Figure 5: Utilities $\widetilde{u_i}$ of two agents in a team, shown as functions of the agent's work units contribution $g_i$ and the rest of the team's contribution $G_{-i}$. Left: Utility for an agent with expertise $p_1^\mathcal{T} = 0.5$. Right: Utility for their teammate with expertise $p_2^\mathcal{T} = 0.8$.

Theorems & Definitions (24)

• Definition 3.1: Generalised Aggregative Game jensen2018aggregative
• Definition 3.2: Best-response correspondence jensen2018aggregative
• Definition 3.3: Replacement Correspondence jensen2018aggregativeacemoglu2013aggregate
• Definition 3.4: Aggregate Replacement Correspondence acemoglu2013aggregate
• Proposition 3.1
• Definition 3.5: Share Correspondence
• Definition 3.6: Normal Good
• Definition 4.1: Unitary Team Task
• Definition 4.2: Expertise Concerning a Unitary Task
• Definition 4.3: Leisure Capacity