Competing Mechanisms in a Common Value Environment

Consider strategic risk‐neutral traders competing in schedules to supply liquidity to a risk‐averse agent who is privately informed about the value of the asset and his hedging needs. Imperfect competition in this common value environment is analyzed as a multi‐principal game in which liquidity suppliers offer trading mechanisms in a decentralized way. Each liquidity supplier behaves as a monopolist facing a residual demand curve resulting from the maximizing behavior of the informed agent and the trading mechanisms offered by his competitors. There exists a unique equilibrium in convex schedules. It is symmetric and differentiable and exhibits typical features of market‐power: Equilibrium trading volume is lower than ex ante efficiency would require. Liquidity suppliers charge positive mark‐ups and make positive expected profits, but these profits decrease with the number of competitors. In the limit, as this number goes to infinity, ask (resp. bid) prices converge towards the upper (resp. lower) tail expectations obtained in Glosten (1994) and expected profits are zero.     

The Bubble Game: An Experimental Study of Speculation

We propose a bubble game that involves sequential trading of an asset commonly known to be valueless. Because no trader is ever sure to be last in the market sequence, the game allows for a bubble at the Nash equilibrium when there is no cap on the maximum price. We run experiments both with and without a price cap. Structural estimation of behavioral game theory models suggests that quantal responses and analogy‐based expectations are important drivers of speculation.     

多再制造商回收定价竞争博弈

多个再制造商在同一回收市场中获取废旧产品并进行再制造,他们之间存在回收竞争.每个再制造商回收废旧产品的数量取决于自身付出的回收价格,同时和对手们的回收价格相关.目标是最大化各自的期望利润.本文首先利用优化理论和非合作博弈理论,证明了该博弈作为超模博弈,存在唯一的Nash均衡.然后通过比较发现竞争下的Nash均衡价格高于串谋下的合作均衡价格.最后通过数值仿真探讨了再制造商的数目和再制造成本对博弈的影响.     

Information in Securities Markets: Kyle Meets Glosten and Milgrom

This paper analyzes models of securities markets with a single strategic informed trader and competitive market makers. In one version, uninformed trades arrive as a Brownian motion and market makers see only the order imbalance, as in Kyle (1985). In the other version, uninformed trades arrive as a Poisson process and market makers see individual trades. This is similar to the Glosten–Milgrom (1985) model, except that we allow the informed trader to optimize his times of trading. We show there is an equilibrium in the Glosten–Milgrom‐type model in which the informed trader plays a mixed strategy (a point process with stochastic intensity). In this equilibrium, informed and uninformed trades arrive probabilistically, as Glosten and Milgrom assume. We study a sequence of such markets in which uninformed trades become smaller and arrive more frequently, approximating a Brownian motion. We show that the equilibria of the Glosten–Milgrom model converge to the equilibrium of the Kyle model.     

Multiperson Bargaining and Strategic Complexity

We investigate the effect of introducing costs of complexity in the n‐person unanimity bargaining game. As is well‐known, in this game every individually rational allocation is sustainable as a Nash equilibrium (also as a subgame perfect equilibrium if players are sufficiently patient and if n & 2). Moreover, delays in agreement are also possible in such equilibria. By limiting ourselves to a plausible notion of complexity that captures length of memory, we find that the introduction of complexity costs (lexicographically with the standard payoffs) does not reduce the range of possible allocations but does limit the amount of delay that can occur in any agreement. In particular, we show that in any n‐player game, for any allocation z, an agreement on z at any period t can be sustained as a Nash equilibrium of the game with complexity costs if and only if t≤n. We use the limit on delay result to establish that, in equilibrium, the strategies implement stationary behavior. Finally, we also show that ‘noisy Nash equilibrium’ with complexity costs sustains only the unique stationary subgame perfect equilibrium allocation.     

最优交易策略对交易持续期的影响

构建一个纯流动市场交易动态策略模型。假设交易者按Poisson过程到达市场,交易者根据其私人估值及市场状态对限价指令的收益做预期,通过最大化其收益确定所提交指令的类型(限价指令或市价指令)。模型发现,虽然交易者到达市场的时间间隔相互独立,但交易持续期却受前一期的交易策略影响:买(卖)指令的提交将增加下一期卖(买)交易持续期的期望值,减小下一期买(卖)交易的持续期的期望值。因而,交易间的自相关性是依据最优交易策略所内生的性质,与知情交易无关。     

A Dynamic Reinterpretation of Nash Bargaining With Endogenous Threats

This paper concerns the two‐stage game introduced in Nash (1953). It formalizes a suggestion made (but not pursued) by Nash regarding equilibrium selection in that game, and hence offers an arguably more solid foundation for the “Nash bargaining with endogenous threats” solution. Analogous reasoning is then applied to an infinite horizon game to provide equilibrium selection in two‐person repeated games with contracts. In this setting, issues about enforcement of threats are much less problematic than in Nash's static setting. The analysis can be extended to stochastic games with contracts.     

Improving Valuation Under Consumer Search: Implications for Pricing and Profits

There is a growing trend in the retail industry to improve customer experience. In this article, we study retailer‐initiated strategies to increase consumer valuation for a product under duopoly. In such a setting, it is possible that a consumer's valuation may be increased by one retailer; however, the consumer may decide to buy the product from the competitor. We consider a two‐stage game where retailers first decide whether to invest in improvements in customer valuation and then engage in price competition. We computationally explore the Nash equilibria in terms of both investment and pricing. We find that in the majority of cases retailers price in a manner to discourage their local customers to buy from the competitor. Next, we focus on the pricing game and theoretically characterize the pricing Nash equilibrium. We find that a retailer could overcome competitive effects by improving consumer valuation beyond a certain threshold. We also find that a retailer who does not invest could benefit from competition in situations where his competitor increases consumer valuation beyond a threshold. Finally, we explore through a computational study the Nash equilibria of the two‐stage game using an alternate model to establish the robustness of our findings.     

Perfect Competition in Markets With Adverse Selection

This paper proposes a perfectly competitive model of a market with adverse selection. Prices are determined by zero‐profit conditions, and the set of traded contracts is determined by free entry. Crucially for applications, contract characteristics are endogenously determined, consumers may have multiple dimensions of private information, and an equilibrium always exists. Equilibrium corresponds to the limit of a differentiated products Bertrand game. We apply the model to establish theoretical results on the equilibrium effects of mandates. Mandates can increase efficiency but have unintended consequences. With adverse selection, an insurance mandate reduces the price of low‐coverage policies, which necessarily has indirect effects such as increasing adverse selection on the intensive margin and causing some consumers to purchase less coverage.     

Modeling Strategic Behavior in The Competitive Newsvendor Problem: An Experimental Investigation

This study experimentally investigates ordering behavior in the competitive newsvendor problem. We consider a duopoly market setting with two identical newsvendors selling the same perishable goods in a common market. Our experimental results show that average observed orders systematically deviate from the Nash equilibrium, and exhibit a similar pull‐to‐center pattern as in the classic non‐competitive newsvendor experiments: average orders fall below the Nash equilibrium in the high‐margin condition, and above the Nash equilibrium in the low‐margin condition. More importantly, the observed orders in the duopoly market are significantly higher than that in the non‐competitive newsvendor market, even in situations where standard inventory models predict no difference. We explain the ordering behavior using a strategic experience‐weighted attraction (EWA) model, which captures players' propensities for strategic thinking in game settings. Our empirical analysis suggests that the strategic EWA model generates more accurate predictions of future ordering behavior than an existing linear adaptive model without concerning strategic thinking. Further analysis shows that individuals are heterogeneous in their propensities to be a strategic player. Our research indicates the importance of modeling strategic behavior when analyzing behavioral decisions in competitive (game) environments.     

股票市场的有限套利：一个行为金融模型

从行为金融的角度,结合有限套利与非理性个体对股票市场的套利者收益、资产价格特征进行考察。通过引入趋势交易者,发展了有限套利模型,并得到了套利者期望收益和市场波动性的解析解。然后对较宽范围内参数的可能取值进行了模拟。结果发现,套利收益同套利者能力和个体交易者的非理性程度有明显的非线性关系,在一定的条件下,套利者不但无法稳定市场,反而会促进资产价格的波动。     

Waiting for News in the Market for Lemons

We study a dynamic setting in which stochastic information (news) about the value of a privately informed seller's asset is gradually revealed to a market of buyers. We construct an equilibrium that involves periods of no trade or market failure. The no‐trade period ends in one of two ways: either enough good news arrives, restoring confidence and markets reopen, or bad news arrives, making buyers more pessimistic and forcing capitulation that is, a partial sell‐off of low‐value assets. Conditions under which the equilibrium is unique are provided. We analyze welfare and efficiency as they depend on the quality of the news. Higher quality news can lead to more inefficient outcomes. Our model encompasses settings with or without a standard static adverse selection problem—in a dynamic setting with sufficiently informative news, reservation values arise endogenously from the option to sell in the future and the two environments have the same equilibrium structure.     

指令驱动市场中非知情交易者的最优交易策略

在非对称信息下,综合非知情交易者对资产价值的预期、私人估值及资产价值波动,构造指令驱动市场价格形成的动态模型,给出非知情交易者指令提交策略的解析解,并依此描述了非知情交易者对资产价值预期的动态更新过程.研究发现:私人估值和资产价值波动通过影响非知情交易者最优策略,使得市场进入不同均衡状态;在每个均衡状态下,非知情交易者根据资产价值的预期变化更新交易策略,进而引起知情交易者策略调整,特别地,使得知情交易者被挤出市场成为可能.进一步分析表明,私人估值、资产价值波动及知情交易者比例对市场流动性的影响依赖于每个均衡中限价指令执行风险的差异.     

Bayesian Learning,Smooth Approximate Optimal Behavior,and Convergence to ε‐Nash Equilibrium

In this paper, I construct players' prior beliefs and show that these prior beliefs lead the players to learn to play an approximate Nash equilibrium uniformly in any infinitely repeated slightly perturbed game with discounting and perfect monitoring. That is, given any ε > 0, there exists a (single) profile of players' prior beliefs that leads play to almost surely converge to an ε‐Nash equilibrium uniformly for any (finite normal form) stage game with slight payoff perturbation and any discount factor less than 1.     

信息不对称条件下双寡头市场中质量差异化产品虚假信息问题研究

基于博弈论和契约理论,研究了信息不对称条件下双寡头市场质量差异化产品定价过程中虚假信息的问题。消费者与企业关于产品质量信息存在严重不对称,为企业使用虚假质量信息提高企业利润提供了较大的空间。为分析企业使用虚假信息的问题,本文基于Bertrand博弈模型构建了双寡头市场质量差异化产品定价模型并求解企业利润。求解结果表明双寡头市场的纳什博弈均衡解为两企业均使用虚假信息,在此基础上进一步从契约的角度对企业使用虚假信息的问题进行了合理规避。最后运用算例分析验证了模型的正确性。     

有限理性下序贯价格竞争的动态演化

本文建立了两个企业的序贯价格竞争模型，基于有限理性预期调整，研究了企业博弈的动态演化特征，分析了模型的均衡解及其稳定性条件。研究发现，边界解和纳什均衡解是一定参数条件下的局部稳定均衡。基于有限理性的动态博弈能够实现基于完全信息的纳什均衡。单纯跟随策略是一定条件下的均衡策略，并能使跟随企业获得更高的销售价格。企业之间报价的相互跟随程度和企业预期的调整速度将会影响均衡点的稳定性。本文对模型进行了数值模拟分析，当参数不满足稳定性条件时会出现分岔、奇异吸引子等混沌现象。本文的主要研究结果对相关行业的企业竞争和稳定市场有启发意义。     

Optimal Dynamic Pricing of Perishable Items by a Monopolist Facing Strategic Consumers

We introduce a dynamic pricing model for a monopolistic company selling a perishable product to a finite population of strategic consumers (customers who are aware that pricing is dynamic and may time their purchases strategically). This problem is modeled as a stochastic dynamic game in which the company's objective is to maximize total expected revenues, and each customer maximizes the expected present value of utility. We prove the existence of a unique subgame‐perfect equilibrium pricing policy, provide equilibrium optimality conditions for both customer and seller, and prove monotonicity results for special cases. We demonstrate through numerical examples that a company that ignores strategic consumer behavior may receive much lower total revenues than one that uses the strategic equilibrium pricing policy. We also show that, when the initial capacity is a decision variable, it can be used together with the appropriate pricing policy to effectively reduce the impact of strategic consumer behavior. The proposed model is computationally tractable for problems of realistic size.     

基于不同预期报价决策的电力市场动态演化及其混沌控制

基于市场参与者不同预期的报价决策方式,提出了考虑输电网约束的电力市场动态模型,即内嵌市场清算优化问题的差分动态模型.该模型刻画出发电方和需求方同时报价的不用决策行为,并准确反映出独立系统调度员ISO的统一市场清算过程,考虑了输电网固有物理特性所赋予电力市场的复杂约束.借助非线性互补函数,对应不同的输电网运行状态:阻塞和不阻塞,分析比较了电力市场处于Nash均衡、周期和混沌的经济表现.针对经济表现差的市场混沌态,提出电力市场状态和参数时滞反馈控制方法,给出电力市场由混沌到Nash均衡的调控措施和手段,从而为有效提高电力市场的经济效益提供了理论依据.     

A Competitive Model of Customization with Lead‐Time Effects

In this article, we study the competitive interactions between a firm producing standard products and a firm producing custom products. Consumers with heterogeneous preferences choose between n standard products, which may not meet their preferences exactly but are available immediately, and a custom product, available only after a certain lead time l. Standard products incur a variety cost that increases with n and custom products incur a lead time cost that is decreasing in the lead time l. We consider a two‐stage game wherein at stage 1, the standard product firm chooses the variety and the custom firm chooses the lead time and then both firms set prices simultaneously. We characterize the subgame‐perfect Nash equilibrium of the game. We find that both firms can coexist in equilibrium, either sharing the market as local monopolists or in a price‐competitive mode. The standard product firm may offer significant or minimal variety depending on the equilibrium outcome. We provide several interesting insights on the variety, lead time, and prices of the products offered and on the impact of problem parameters on the equilibrium outcomes. For instance, we show that the profit margin and price of the custom product are likely to be higher than that of standard products in equilibrium under certain conditions. Also, custom firms are more likely to survive and succeed in product markets with larger potential market sizes. Another interesting insight is that increased consumer sensitivity to product fit may result in lower lead time for the custom product.     

Competition for a Majority

We define the class of two‐player zero‐sum games with payoffs having mild discontinuities, which in applications typically stem from how ties are resolved. For such games, we establish sufficient conditions for existence of a value of the game, maximin and minimax strategies for the players, and a Nash equilibrium. If all discontinuities favor one player, then a value exists and that player has a maximin strategy. A property called payoff approachability implies existence of an equilibrium, and that the resulting value is invariant: games with the same payoffs at points of continuity have the same value and ɛ‐equilibria. For voting games in which two candidates propose policies and a candidate wins election if a weighted majority of voters prefer his proposed policy, we provide tie‐breaking rules and assumptions about voters' preferences sufficient to imply payoff approachability. These assumptions are satisfied by generic preferences if the dimension of the space of policies exceeds the number of voters; or with no dimensional restriction, if the electorate is sufficiently large. Each Colonel Blotto game is a special case in which each candidate allocates a resource among several constituencies and a candidate gets votes from those allocated more than his opponent offers; in this case, for simple‐majority rule we prove existence of an equilibrium with zero probability of ties.