Strategic Delay and Coordination Efficiency in Global Games

Shinkyu Park; Behrouz Touri; Marcos M. Vasconcelos

cs.GTApr 7, 2026

Strategic Delay and Coordination Efficiency in Global Games

Authors: Shinkyu Park, Behrouz Touri, Marcos M. Vasconcelos

Organizations: Electrical and Computer Engineering, King Abdullah University of Science and Technology, Thuwal, 23955, Saudi Arabia · Department of Industrial and Systems Engineering, University of Illinois Urbana Champaign, Champaign, IL 61820 · Department of Electrical and Computer Engineering, FAMU-FSU College of Engineering, Florida State University, Tallahassee, FL 32306, USA

Abstract

We investigate a coordination model for a two-stage collective decision-making problem within the framework of global games. The agents observe noisy signals of a shared random variable, referred to as the fundamental, which determines the underlying payoff. Based on these signals, the agents decide whether to participate in a collective action now or to delay. An agent who delays acquires additional information by observing the identities of agents who have chosen to participate in the first stage. This informational advantage, however, comes at the cost of a discounted payoff if coordination ultimately succeeds. Within this decision-making framework, we analyze how the option to delay can enhance collective outcomes. We show that this intertemporal trade-off between information acquisition and payoff reduction can improve coordination and increase the efficiency of collective decision-making.

Figures & tables

Fig. 1: Two-stage global game with public (noiseless) feedback signal. In the first stage, the blue nodes decided to take the risky action, and the white nodes delayed their decision to the second stage. In the second stage the purple nodes decided to take the risky action. The payoff is collected at the end of the game.

\mathbb{E}\!\left[\frac{1}{N}\Bigg(\sum_{j\neq i}\mathbb{1}(Y_{j}\leq\max\{\tau^{\star},\lambda^{\star}(S)\})+1\Bigg)\!-\!\Theta\,\Bigg|\,Y_{i}\!=\!y_{i}\right]\\ \geq\gamma\mathbb{E}\Bigg[\mathbb{1}(Y_{i}\leq\lambda^{\star}(S))\left(\frac{1}{N}\left(\sum_{j\neq i}\mathbb{1}(Y_{j}\!\leq\!\max\{\tau^{\star},\lambda^{\star}(S)\})\right)\!+\!1\right)\!-\!\Theta\Bigg|\,Y_{i}\!=\!y_{i}\Bigg],

(8)

Table 2

\frac{1}{N}\left(\sum_{j\notin\mathcal{S}\cup\{i\}}\mathbb{E}\!\Big[\mathbb{1}(Y_{j}\leq\max\{\tau^{\star},\lambda^{\star}(S)\})\ \Big|\ Y_{j}>\tau^{\star},Y_{i}=y_{i},S=s\Big]+1\right)+s-\mathbb{E}\Big[\Theta\ \Big|\ Y_{i}=y_{i},S=s\Big]\geq 0

(11)

Table 3

Fig. 2: Per agent welfare for a two-stage global game with

\gamma=0.8

Fig. 3: Illustration of the function $V(\sigma,\gamma)$ defined in ( 35 ). The red region indicates the parameter regime $(\sigma,\gamma)$ in which the option to delay is beneficial, whereas the blue region corresponds to regimes in which it is detrimental.

\Delta^{N}(y_{i})\Equaldef\mathbb{E}\!\left[\frac{1}{N}\left(\sum_{j\neq i}\mathbb{1}(Y_{j}\leq\max\{\tau_{\text{single}}^{\star},\lambda^{\star}(S)\})+1\right)-\Theta\ \Bigg|\ Y_{i}=y_{i}\right]\\ -\gamma\,\mathbb{E}\!\left[\mathbb{1}(Y_{i}\leq\lambda^{\star}(S))\left(\frac{1}{N}\left(\sum_{j\neq i}\mathbb{1}(Y_{j}\leq\max\{\tau_{\text{single}}^{\star},\lambda^{\star}(S)\})+1\right)-\Theta\right)\ \Bigg|\ Y_{i}=y_{i}\right].

(39)

Table 6

\Delta^{N}(y_{i})\geq\mathbb{E}\!\left[\frac{1}{N}\left(\sum_{j\neq i}\mathbb{1}(Y_{j}\leq\max\{\tau_{\text{single}}^{\star},\lambda^{\star}(S)\})+1\right)-\Theta\ \Bigg|\ Y_{i}=y_{i}\right]\\ \hskip 8.50012pt-\gamma\sup_{y_{i}}\,\mathbb{E}\!\left[\frac{1}{N}\left(\sum_{j\neq i}\mathbb{1}(Y_{j}\leq\max\{\tau_{\text{single}}^{\star},\lambda^{\star}(S)\})+1\right)-\Theta\ \Bigg|\ Y_{i}=y_{i}\right]\\ >\mathbb{E}\!\left[\frac{1}{N}\left(\sum_{j\neq i}\mathbb{1}(Y_{j}\leq\tau_{\text{single}}^{\star})+1\right)-\Theta\ \Bigg|\ Y_{i}=y_{i}\right]\geq 0.

(40)

Table 7

\Delta^{N}(y_{i})=\mathbb{E}\!\left[\frac{1}{N}\left(\sum_{j\neq i}\mathbb{1}(Y_{j}\leq\max\{\tau_{\text{single}}^{\star},\lambda^{\star}(S)\})+1\right)-\Theta\ \Bigg|\ Y_{i}=y_{i}\right]>\mathbb{E}\!\left[\frac{1}{N}\left(\sum_{j\neq i}\mathbb{1}(Y_{j}\leq\tau_{\text{single}}^{\star})+1\right)-\Theta\ \Bigg|\ Y_{i}=y_{i}\right]\geq 0.

(41)

Table 8

\Delta^{N}(y_{i})=(1-\gamma)\,\mathbb{E}\!\left[\frac{1}{N}\left(\sum_{j\neq i}\mathbb{1}(Y_{j}\leq\max\{\tau_{\text{single}}^{\star},\lambda^{\star}(S)\})+1\right)-\Theta\ \Bigg|\ Y_{i}=y_{i}\right]\\ >(1-\gamma)\,\mathbb{E}\!\left[\frac{1}{N}\left(\sum_{j\neq i}\mathbb{1}(Y_{j}\leq\tau_{\text{single}}^{\star})+1\right)-\Theta\ \Bigg|\ Y_{i}=y_{i}\right]\geq 0.

(42)

Table 9

Multi-Agent Coordination

Multi-agent coordination studies how autonomous agents align actions, share information, and divide work to achieve individual or collective goals.

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Multi-Agent Decision-Focused Learning via Value-Aware Sequential Communication

Benjamin Amoh, Geoffrey Parker, Wesley Marrero

Thayer School of Engineering, Dartmouth College

Multi-Agent Coordination Multi-Agent Communication Cooperative MARL Decision-Focused Learning Partially Observable RL

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Multi-agent coordination under partial observability requires agents to share complementary private information. While recent methods optimize messages for intermediate objectives (e.g., reconstruction accuracy or mutual information), rather than decision quality, we introduce SeqComm-DFL, unifying the sequential communication with decision-focused learning for task performance. Our approach features value-aware message generation with sequential Stackelberg conditioning: messages maximize receiver decision quality and are generated in priority order, with agents conditioning on their predecessors. The guidance potential determined by their prosocial ordering. We extend Optimal Model Design to communication-augmented world models with QMIX factorization, enabling efficient end-to-end training via implicit differentiation. We prove information-theoretic bounds showing that communication value scales with coordination gaps and establish

\mathcal{O}(1/\sqrt{T})

convergence for the bilevel optimization, where

T

denotes the number of training iterations. On collaborative healthcare and StarCraft Multi-Agent Challenge (SMAC) benchmarks, SeqComm-DFL achieves four to six times higher cumulative rewards and over 13% win rate improvements, enabling coordination strategies inaccessible under information asymmetry.

Abstract

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