以代理人基模型模擬的施與受賽局

Abstract

人類合作造成的社會影響與個人影響是社會科學的一個重要問題。最近提出了一個動態可調整的合作策略和不同聲譽的衡量規範的個人社會模型 [1]。為了將平均場分析結果作進一步解析，我們以代理人基模型進行電腦計算模擬。在模型中的每一位代理人實施的策略調整，均由社會學習模式來決定，類似在Potts模型下Metropolis能量驅動的狀態轉換。在施與受賽局演化模型中，社會由許多代理人組成，每一個代理人會隨機遇到另一個代理人，雙方共同合作，構成捐贈方及受援方的成對組合。在給定捐贈方的策略及受援方的評價後，捐贈方每一回合遊戲可以採取合作或不合作，與加入懲罰的三種策略。在遊戲試驗進行中，根據各種策略已經給定合作的交易成本與收益以及懲罰的成本與損失，在每一回合遊戲進行結束後，捐贈方將被重新給定評價，並且計算全體代理人的財富變化。在連續進行的遊戲中，代理人會根據每個代理人與社會群體的財富變化，產生知識累積的學習模式，作為策略轉換權數的基準。在以類比於自旋翻換模型於溫度零度的模擬下，我們對此社會模型代理人策略採取的演化模式，得到了一些初步觀察的結果。使用代理人基模型模擬三種社會規範：簡單社會規範（無懲罰的社會規範），弱懲罰社會規範（允許懲罰的社會規範）與強懲罰的社會規範（加強懲罰的社會規範）與平均場理論作初步比較。模擬結果得出與原先平均場理論一致的結論：主要解與第一次要解均相同，懲罰將促進合作，並在強懲罰社會規範下存在第二次要解。\n在代理人基模型的各代理人是以社會學習模式後採取更新策略。社會學習與個人學習的差異在於，每一位代理人賽局累積經驗作為學習的樣本來自於社會全體代理人還是只有自己。在賽局中各代理人的所得與財富將依照代理人在每一回合賽局中的身份與策略產生變動，對此變動計數在分別以兩種模式：簡單平均（人數權重法）與權重平均（事件權重法）計算平均法得出，簡單平均法產生唯一主要解，權重平均法將差異保留，主要解與次要解共存。我們發現代理人基模型中最終狀態的次要解，除了可能以其所有成員都為好人的合諧社會的型式出現外，也可能是以極限軌道而非離散點的新型態出現。\n\n[1] Tongkui Yu, Shu-heng Chen, Honggang Li, "Social Norm, Costly Punishment and the Evolution to Cooperation," 17th International Conference on Computing in Economics and Finance.

The effects of human cooperation on the societies and on the individuals is an important issue in social science. The dynamics of a model society of individuals with adjustable cooperation strategies and with varying reputations gauged by social norms has been recently proposed [1]. In order to refine the mean-field type analysis, we implement the Agent-based model in computer simulations, where the strategy adjustment of each individual is determined by a social learning procedure. In between consecutive strategy changes, one individual encounters a partner in a Donor-Recipient game, which results in the wealth changes in both parties in form of cost, punishment or benefit and is followed by a reputation re-assignment to the donor, taking into account the strategy of the donor and the reputation of the recipient. The accumulated knowledge of wealth changes from sequences of games for all individuals in the society weighs the strategy change transitions. We obtain some primitive observations on the evolutions of strategies adapted by the individuals of the model society. Using the agent-based models to simulate three kinds of social norms: Simple social norm (punishment-free social norm), Weakly augmented social norm (punishment-optional social norm) and Strongly augmented social norm (punishment-provoking social norm). We try to compare the outcome of the agent-based model with the solutions of mean-field equation. The two methods are found to have unanimous results: they have the same the primary solution and the main secondary solution; punishment would promote cooperation and social norms in strong penalties exist under the second secondary solution. In contrast to the mean-field scenario, the players in the agent based model update their strategies asynchronously, based on the accumulated knowledge of wealth changes for players adapting each strategy. We distinguish the models of two modules of such knowledge, learned either by simple averages (player-weighted method) or by weighted averages (event-weighted method). In carrying out the zero-temperature analogy of spin-flipping simulation, we obtain some primitive observations on the strategy evolution of the agents. While all solutions of the mean field equations are consistently obtained in the latter case, only the primary solution is found for the former case in each social norm. It is found that a minor stable attractor may survive in the time evolution which are ported by harmonious societies, where all agents are reputed as “good”. In the time evolution, the competition between strategies may display the presence of dynamic orbits as the final domain of time evolution.\n\n[1] Tongkui Yu, Shu-heng Chen, Honggang Li, "Social Norm, Costly Punishment and the Evolution to Cooperation," 17th International Conference on Computing in Economics and Finance.