不完全訊息下經濟體系之穩定性分析

Abstract

本論文主要探討，賽局理論中，參賽者存在不完全訊息時，反而可以增加賽局結果(outcome)之穩定性。論文第一部分主要說明，在 不全完訊息動態賽局，參賽者可以藉由learning rule增加賽局結果與Nash均衡一致的機率。論文第二部分為不全完訊息靜態模型，分析銀行藉由同業互相存款，降低存款戶擠兌導至銀行倒閉之機率。 賽局理論中，經濟學家最關心之議題莫過於均衡為何。均衡之所以重要，主要因參賽者(players)可依據均衡之集合作最佳回應，因此均衡集合可以提供分析賽局結果之方向。相較於均衡，部分經濟學家更關心參賽者們所選擇的賽局結果是否與均衡一致。賽局存在唯一均衡時，賽局結果與均衡具有一致性;賽局存在多重均衡時，若沒有給予更多的限制，賽局結果將與Nash均衡不具有一致性。第一部分有二個議題，第一個議題為:在 合作賽局中，長期之下outcome path是否收斂且其極值之特性。第二個議題為：在 不全完訊息賽局中，參賽者的行為存在慣性時，是否可以增加outcome path收斂的機率? 在第二章中，主要探討在 合作賽局中，穩定均衡之特性。我們假設每位參賽者皆相信其對手採用 adaptive learning。因此參賽者可以藉由experiment test引導對手選擇Pareto efficient equilibrium。期末若對手的決策與參賽者預期不一致時，參賽者可推測其對手存在犯錯的機率。當參賽者將對手犯錯的機率納入模型中，卻極大化終身效用時，我們得到主要的結論為：玩家較有耐性時（折現率值(discount rate)較小），Pareto efficient equilibrium較risk dominant equilibrium 穩定;反之，risk dominant equilibrium較穩定。 在不全完訊息賽局中，參賽局可以透過Bayesian Learning來更新其資訊。在動態賽局過程中，每一期皆存在新的訊息，供參賽者更正對手的資訊。當參賽者改變其最佳策略時，表示參賽者將選擇期望報酬較低的均衡。第三章主要探討，在 不完全訊息賽局中，參賽者的報酬為均等分配時，若參賽者一開始皆採用Bayesian Learning，在動態過程參賽者的行為存慣性，是否可以增加outcome path收斂的機率且與Nash均衡具有一致。慣性行為定義為當參賽者需改變最佳策略時，其仍採用上一期的策略，以增加停留在預期報酬較高的均衡。本章發現當參賽者的行為存在慣性時，可以減少Jadon (1993) outcome path與Nash均衡不一致之問題。 銀行主要功能為資金之仲介，提高了資金的流動性，協助經濟發展。銀行面對提款率的不確定性。當取款率大於銀行保留準備率時，銀行需立即拋售部分資產換取現金，以應付超額的提款。即時取回投資資金，需承擔較大的折現率，可能導致其它存款戶預期銀行未來的還款能力不足，進而造成存款者擠兌。第四章，我們假設銀行面對提款率不確定性，銀行可以藉由同業互相存款來增加還款能力之降低銀行倒閉的機率。不同文獻，本章假設銀行同業互相存款為內生，而非外生給定。本章得到的主要結論為: (1)、銀行同業互相存款可降低銀行倒閉的機率;(2)、最佳網絡為環狀網絡(Wheel Network)。

Individuals usually interact with others and react to their circumstances. They form their expectations about nature or their counterparts, and base on such beliefs, make decisions or choose strategies in order to maximize their utility. The outcomes of their interaction form part of the histories that again influence individuals' actions in the next period, and so on. In situations where individuals only have partial information about their environments, we usually assume that through repeated interactions, players may learn more information and update beliefs so that they may form satisfactory strategies to improve their payoffs. In this dissertation, I propose to extend above techniques to apply to the dynamic state and static state of the incomplete information game. Young (1993) and KMR (1993) show that risk dominant equilibrium is stochastically stable equilibrium in 2×2 symmetric coordination games where players adopt adaptive learning to play the game. In the adaptive learning dynamics, players are myopic such that they maximize the current expected payoffs for given beliefs formed from past histories. In reality, players may have strategic consideration to influence others' choices of actions and thus to improve their own payoffs. In chapter 2, we modify the learning rule as experimental learning in which each player expects that her opponent adopts adaptive learning and she best responds to such a belief to maximize her lifetime payoff. We find that if players are sufficiently patient, Pareto efficient equilibrium will be selected. The reason is that fewer mutations occurring in risk dominant equilibrium suffices to provide incentives for a player to try more experimentations to 'persuade' her opponent to switch to the efficient equilibrium as discount factor becomes larger. In incomplete information games, players can update their beliefs and actions through Bayesian Learning. As the game proceeds and more players' choices are realized, players will in general have sharper prediction on opponents' types. Once a player's best response of BNE differs from the last one, this implies the player needs to choose the other equilibrium. With small variation of beliefs on the opponent's types, a player usually sticks to the same action best responding to such a belief. In chapter 3, we consider action inertia in the Bayesian Strategy Process to study the stable outcome of 2×2 Bayesian games. Action inertia is that the player replicate last-period action instead of revising her action to an opposite dominant equilirium. We find that action inertia can mitigate the unstable outcome problem of Jordan (1991), and the probability of stable outcome increases with the difference of inertial durations as the prior distribution is uniform. Liquidity shock is one of factors to induce a bank to fail. In capter 4, we investigate what is the optimal network in the uncertain banking system. Our model endogenizes the deposits among banks, such that each bank can integrate the aggregate bailout of the banking system to decrease the failure probability. Two main results are as follows. First, in the robust network set, the probability of financial crisis contagions is zero. Second, if the idiosyncratic liquidity shock satisfies uniform distribution, then the wheel network is the optimal structure in the symmetric-network set. Because the bank's profit is discontinuous and decreases with the liquidity shock, i.e. the bank's profit increases with the distance from the healthy bank to the troubled bank. In chapter 5 is the conclusion.