在本文中，我們提出了一種涉及n 個代理的貝葉斯博弈來解決
資源分配問題。我們的主要目標是確定在此上下文中每個代理的
最佳資源分配。
為了實現這一目標，我們首先開發了一個回報函數，作為代理
評估其行為的可取性的參考點。條件預期收益是通過考慮獨立隨
機變量之和的概率來計算的，並優先考慮最小的請求。我們利用
馬爾可夫不等式和切爾諾夫界限等近似來估計此計算過程中的概
率。
此外，我們引入了最佳響應的概念，它將條件預期收益轉化為
微分方程。通過求解這個方程並確定均衡策略，我們可以有效地
確定每個智能體的資源分配。
另外，我們還提出了數值結果，說明了遊戲中均衡策略隨著代
理數量和可用容量變化的變化。這些結果與其他資源分配方案進
行了比較，清楚地證明了我們的方法相對於其他方法的優越性。

In this paper, we propose a Bayesian game involving n agents to tackle
the resource allocation problem. Our main goal is to determine the optimal
distribution of resources for each agent within this context.
To accomplish this, we initially develop a payoff function that acts
as a reference point for agents to evaluate the desirability of their actions.
The conditional expected payoff is computed by considering the
probability of the sum of independent random variables, prioritizing the
smallest requests. We utilize approximations such as Markov’s Inequality
and the Chernoff Bound to estimate the probability in this calculation
process.
Moreover, we introduce the concept of the best response, which transforms
the conditional expected payoff into a differential equation. By
solving this equation and identifying the equilibrium strategy, we can
effectively determine the allocation of resources for each agent.
Additionally, we present numerical findings that illustrate the variability
of the equilibrium strategy in our game as the number of agents
and the available capacity change. These results are compared against
other resource allocation schemes, clearly demonstrating the superiority
of our method over the alternatives.

中文摘要i
Abstract ii
Acknowledgments iii
List of Figures vi
List of Tables vii
1 Introduction 1
2 A Resource Allocation Game 6
3 Equilibrium Strategy 8
3.1 Markov’s Inequality 11
3.2 Chernoff Bound 14
4 Numerical Studies 17
4.1 Resource Allocation with Different Capacity and Number of Agents 18
4.2 Comparison of Different Resource Allocation Strategies 24
5 Conclusions 27
Bibliography 28

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