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Even-Split Strategy in Sequential Colonel Blotto Games 连续上校Blotto游戏中的均分策略
ERN: Stochastic & Dynamic Games (Topic) Pub Date : 2021-10-22 DOI: 10.2139/ssrn.3947995
Xinmi Li, Jie Zheng
{"title":"Even-Split Strategy in Sequential Colonel Blotto Games","authors":"Xinmi Li, Jie Zheng","doi":"10.2139/ssrn.3947995","DOIUrl":"https://doi.org/10.2139/ssrn.3947995","url":null,"abstract":"Klumpp, Konrad, and Solomon (2019, GEB) showed that in a two-player sequential Colonel Blotto game with majoritarian objective, for a large class of contest success functions, there is a unique pure strategy Subgame Perfect Nash Equilibrium characterized by even-split strategy. We generalize this work to multi-player sequential Colonel Blotto games with prize functions where any contestant’s prizes only depend on this contestant’s own number of winning rounds. We show that with weakly monotonic prize functions and CSFs satisfying decreasing success rate condition, there exists a Subgame Perfect Nash Equilibrium supported by the even-split strategy profile. We also show that with strictly monotonic prize functions, even-split strategy profile is the unique Subgame Perfect Nash Equilibrium for Tullock CSFs with r <=1. In a constant-sum game, if there are only 2 contestants with CSFs satisfying decreasing success rate condition, or if there are more than 2 contestants with Tullock CSF r<=1, then weakly monotonic prize functions result in uniqueness of pure strategy Subgame Perfect Nash Equilibrium before any contestant reaches a settled prize. Our work extends Klumpp et al. (2019)’s result in three aspects: prize structure, number of contestants and uniqueness of pure strategy Subgame Perfect Nash Equilibrium. Our work provides a better understanding on the applicability of the simple even-split strategy in Colonel Blotto games where equilibrium strategies are typically complex.","PeriodicalId":319981,"journal":{"name":"ERN: Stochastic & Dynamic Games (Topic)","volume":"56 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121130006","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Following the Customers: Dynamic Competitive Repositioning 跟随客户:动态竞争再定位
ERN: Stochastic & Dynamic Games (Topic) Pub Date : 2020-12-22 DOI: 10.2139/ssrn.3695318
Z. Ning, J. M. Villas-Boas
{"title":"Following the Customers: Dynamic Competitive Repositioning","authors":"Z. Ning, J. M. Villas-Boas","doi":"10.2139/ssrn.3695318","DOIUrl":"https://doi.org/10.2139/ssrn.3695318","url":null,"abstract":"We consider dynamic repositioning when competing firms try to follow the evolution of consumer preferences while taking into account the competitive interaction, both in terms of static market competition and the dynamic effects of different firm positionings. We fully characterize the dynamic market equilibrium, which includes the timing of the firms’ repositionings depending on consumer preferences. As consumer preferences evolve away from where both firms are located, one firm first moves to follow consumer preferences, with the second firm only moving if the consumer preferences continue evolving away from that firm. The model predicts rich market dynamics, where firms stay for some period in different positionings if consumer preferences are in a relatively middle ground or where a firm repositions to follow consumer preferences but then repositions back to the original position if consumer preferences return. We find that, when the variability of the consumer preferences or the discount rate is greater or when the importance of the repositioning attribute is smaller, firms are less likely to follow consumer preferences. Firms are more heterogeneous in their responses, which leads to longer periods of differentiation when the variability of the consumer preferences, the discount rate, or the importance of the repositioning attribute increases. We also find that competing firms reposition less frequently than what is socially optimal and what collusion would imply, and we find more differentiation under collusion than under competition. This paper was accepted by Matthew Shum, marketing.","PeriodicalId":319981,"journal":{"name":"ERN: Stochastic & Dynamic Games (Topic)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130227217","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 5
Spoofing in Equilibrium 均衡欺骗
ERN: Stochastic & Dynamic Games (Topic) Pub Date : 2020-12-03 DOI: 10.2139/ssrn.3742327
Basil Williams, Andrzej Skrzypacz
{"title":"Spoofing in Equilibrium","authors":"Basil Williams, Andrzej Skrzypacz","doi":"10.2139/ssrn.3742327","DOIUrl":"https://doi.org/10.2139/ssrn.3742327","url":null,"abstract":"We present a model of dynamic trading with exogenous and strategic cancellation of orders. We define spoofing as the strategic placing and canceling of orders in order to move prices and trade later in the opposite direction. We show that spoofing can occur in equilibrium. Consistent with regulator concerns, we show that spoofing slows price discovery, raises bid-ask spreads, and raises return volatility. A novel prediction is that the prevalence of equilibrium spoofing is single-peaked in the measure of informed traders, suggesting that spoofing should be more prevalent in markets of intermediate liquidity. We consider within-market and cross-market spoofing and discuss how regulators should allocate resources towards cross-market surveillance.","PeriodicalId":319981,"journal":{"name":"ERN: Stochastic & Dynamic Games (Topic)","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131361490","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
Financing the Litigation Arms Race 为诉讼军备竞赛融资
ERN: Stochastic & Dynamic Games (Topic) Pub Date : 2020-11-01 DOI: 10.2139/ssrn.3719238
Samuel Antill, Steven R. Grenadier
{"title":"Financing the Litigation Arms Race","authors":"Samuel Antill, Steven R. Grenadier","doi":"10.2139/ssrn.3719238","DOIUrl":"https://doi.org/10.2139/ssrn.3719238","url":null,"abstract":"Using a dynamic model of litigation, we show that the increasingly popular practice of third-party litigation financing has ambiguous welfare implications. A defendant and a plaintiff bargain over a settlement payment. The defendant takes costly actions to avoid deadweight losses associated with large transfers to the plaintiff. Litigation financing bolsters the plaintiff, leading to larger deadweight losses. However, by endogenously deterring the defendant from taking costly actions, litigation financing can nonetheless improve the joint surplus of the plaintiff and the defendant. In contrast to popular opinion, litigation financing does not necessarily encourage high-risk frivolous lawsuits.","PeriodicalId":319981,"journal":{"name":"ERN: Stochastic & Dynamic Games (Topic)","volume":"121 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128259274","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 5
Moral Hazard Under Contagion 传染下的道德风险
ERN: Stochastic & Dynamic Games (Topic) Pub Date : 2020-06-30 DOI: 10.2139/ssrn.3847105
Boli Xu
{"title":"Moral Hazard Under Contagion","authors":"Boli Xu","doi":"10.2139/ssrn.3847105","DOIUrl":"https://doi.org/10.2139/ssrn.3847105","url":null,"abstract":"We study dynamic partnerships where the output evolves stochastically, each player can exit at any time, and players who have exited continue to enjoy some benefits of the partnership. We analyze the contagion of defections and show that severe contagion facilitates cooperation among players by deterring free-riding. The unique equilibrium features a curse of productivity, namely, a larger output of the partnership may harm all players by exacerbating free-riding. Another main finding is that a partnership's ability to sustain cooperation is non-monotonic in its size.","PeriodicalId":319981,"journal":{"name":"ERN: Stochastic & Dynamic Games (Topic)","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122078357","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Winner-Leave Versus Loser-Leave in Multi-Stage Nested Tullock Contests 多阶段嵌套图洛克竞赛中的胜者离开与败者离开
ERN: Stochastic & Dynamic Games (Topic) Pub Date : 2020-06-20 DOI: 10.2139/ssrn.3631730
Jingfeng Lu, Yuanzhu Lu, Zhewei Wang, Lixue Zhou
{"title":"Winner-Leave Versus Loser-Leave in Multi-Stage Nested Tullock Contests","authors":"Jingfeng Lu, Yuanzhu Lu, Zhewei Wang, Lixue Zhou","doi":"10.2139/ssrn.3631730","DOIUrl":"https://doi.org/10.2139/ssrn.3631730","url":null,"abstract":"In this paper, we compare two procedures for allocating a sequence of fixed prizes in multi-stage nested Tullock contests, in which the number of prizes equals the number of contestants. In a winner-leave (loser-leave) procedure, in each stage, the prizes of the stage are allocated to winners (losers) according to their ranks, and prizes in early stages are higher (lower) than those in later stages. Players who obtain prizes leave the contest and the others proceed to the next stage of competition. For both procedures, it is effort-maximizing to allocate one prize in each stage. Provided that the positive prizes in the sequence are homogeneous, the optimally designed loser-leave procedure generates higher total effort if and only if the number of positive prizes is lower than a threshold. If the positive prizes in the sequence are heterogeneous, then the loser-leave procedure may generate higher total effort, even if the number of positive prizes in the sequence is in the high range.","PeriodicalId":319981,"journal":{"name":"ERN: Stochastic & Dynamic Games (Topic)","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133605040","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Long-Run Market Configurations in a Dynamic Quality-Ladder Model with Externalities 考虑外部性的动态质量阶梯模型中的长期市场配置
ERN: Stochastic & Dynamic Games (Topic) Pub Date : 2020-02-10 DOI: 10.2139/ssrn.2563585
M. Samano, Marc Santugini
{"title":"Long-Run Market Configurations in a Dynamic Quality-Ladder Model with Externalities","authors":"M. Samano, Marc Santugini","doi":"10.2139/ssrn.2563585","DOIUrl":"https://doi.org/10.2139/ssrn.2563585","url":null,"abstract":"We analyze the type of market structures that arise in the long-run when quality externalities and asymmetric R&D capabilities exist in the context of a quality-ladder dynamic model. An example of such externalities is a patent release by the leading fi rm: an improvement of quality of this firm's good a ects the quality of the other fi rms' products. This externality can be thought of as an increase in compatibility in a network. We show that it is possible for this model to generate, in the long-run, multi-modal probability distributions over di fferent market structures from the same parameter values. In some cases, the lagging rm may even become the dominant fi rm depending on the degree of the externality. This may have implications for the estimation and simulation of this class of models.","PeriodicalId":319981,"journal":{"name":"ERN: Stochastic & Dynamic Games (Topic)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131031567","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Prediction and Stochastic Choice 预测与随机选择
ERN: Stochastic & Dynamic Games (Topic) Pub Date : 2019-04-20 DOI: 10.2139/ssrn.3338991
Pathikrit Basu
{"title":"Prediction and Stochastic Choice","authors":"Pathikrit Basu","doi":"10.2139/ssrn.3338991","DOIUrl":"https://doi.org/10.2139/ssrn.3338991","url":null,"abstract":"In this paper, we study a non-parametric approach to prediction in stochastic choice models in economics. We show that VC complexity characterises the predictability of stochastic choice models. We establish prediction methods and provide corresponding rates of convergence.<br>","PeriodicalId":319981,"journal":{"name":"ERN: Stochastic & Dynamic Games (Topic)","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124962556","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Dynamic Valuation of Callable Contingent Claims With a Partially Observable Regime Switch 具有部分可观察状态切换的可赎回或有债权的动态估值
ERN: Stochastic & Dynamic Games (Topic) Pub Date : 2018-11-14 DOI: 10.2139/ssrn.3284489
Kimitoshi Sato, K. Sawaki
{"title":"The Dynamic Valuation of Callable Contingent Claims With a Partially Observable Regime Switch","authors":"Kimitoshi Sato, K. Sawaki","doi":"10.2139/ssrn.3284489","DOIUrl":"https://doi.org/10.2139/ssrn.3284489","url":null,"abstract":"In this paper, we consider a model for valuing callable financial securities when the underlying asset price dynamic is unobservable but can be partially observed by receiving a signal stochastically related to the state of the real economy. In callable securities, both the issuer and the investor have the right to call. We formulate this problem as a coupled stochastic game for the optimal stopping problem within a partially observable Markov decision process. We show that there exists a unique optimal value for the callable contingent claim, and it is a unique fixed point of a contraction mapping. We derive analytical properties of the optimal stopping rules for the issuer and the investor under two types (put and call) of general payoff functions. We provide a numerical example to illustrate specific stopping boundaries for each player; this is done by specifying the payoff function of the callable securities.","PeriodicalId":319981,"journal":{"name":"ERN: Stochastic & Dynamic Games (Topic)","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130261662","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Exploration vs Exploitation, Impulse Balance Equilibrium, and a Specification Test for the El Farol Bar Problem 勘探与开发、脉冲平衡平衡和El Farol Bar问题的规范检验
ERN: Stochastic & Dynamic Games (Topic) Pub Date : 2018-08-16 DOI: 10.2139/ssrn.3233147
A. Kirman, François Laisney, Paul Pezanis-Christou
{"title":"Exploration vs Exploitation, Impulse Balance Equilibrium, and a Specification Test for the El Farol Bar Problem","authors":"A. Kirman, François Laisney, Paul Pezanis-Christou","doi":"10.2139/ssrn.3233147","DOIUrl":"https://doi.org/10.2139/ssrn.3233147","url":null,"abstract":"The paper reports on market-entry experiments that manipulate both payoff structures and payoff levels to assess two stationary models of behaviour: Exploration vs Exploitation (EvE, which is equivalent to Quantal Response Equilibrium) and Impulse Balance Equilibrium (IBE). These models explain the data equally well in terms of goodness-of-fit whenever the observed probability of entry is less than the symmetric Nash equilibrium prediction; otherwise IBE marginally outperforms EvE. When assuming agents playing symmetric strategies, and estimating the models with session data, IBE yields more theory-consistent estimates than EvE, no matter the payoff structure or level. However, the opposite occurs when the symmetry assumption is relaxed. The conduct of a specification test rejects the validity of the restrictions on entry probabilities imposed by EvE for agents with symmetric strategies, in 50 to 75% of sessions and it always rejects it in the case of IBE, which indicates that the symmetric variant of these models has little empirical support.","PeriodicalId":319981,"journal":{"name":"ERN: Stochastic & Dynamic Games (Topic)","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131657072","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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