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"Spiel"
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Designing Dynamic Contests
Firms and institutions increasingly employ
contests
as a way to innovate. Participants learn from one another’s successes and failures while competing for the contest’s awards. In “Designing Dynamic Contests,” Bimpikis, Ehsani, and Mostagir provide a number of design guidelines that focus on the contest’s information-disclosure policy. Critically, their analysis highlights that, when agents compete and learn from one another dynamically, the success of the contest largely relies on
when
and
what
information the designer chooses to disclose about their relative progress toward the end goal.
Participants race toward completing an innovation project and learn about its feasibility from their own efforts and their competitors’ gradual progress. Information about the status of competition can alleviate some of the uncertainty inherent in the contest, but it can also adversely affect effort provision from the laggards. This paper explores the problem of designing the award structure of a contest and its information disclosure policy in a dynamic framework and provides a number of guidelines for maximizing the designer’s expected payoff. In particular, we show that the probability of obtaining the innovation as well as the time it takes to complete the project are largely affected by
when
and
what
information the designer chooses to disclose. Furthermore, we establish that intermediate awards may be used by the designer to appropriately disseminate information about the status of competition. Interestingly, our proposed design matches several features observed in real-world innovation contests.
The e-companion is available at
https://doi.org/10.1287/opre.2018.1823
.
Journal Article
Ringbearers : The Lord of the Rings Online as intertextual narrative
Ringbearers\" collects together essays by established and leading figures within Game Studies, each focused on different aspects of the Massively Multiplayer Online game \"The Lord of the Rings Online\". The collection is essential reading for those looking to better understand the adaptation into online game form of Tolkien's fictional world, as well as those seeking to comprehend the design and uses of online games. This makes \"Ringbearers\" an ideal textbook for students and scholars of interactive fictional media. The authors played the game extensively, yet they each come to it with different questions. Some essays focus on what players do with and in the game, whether that means asking about the opportunities provided for role-play or asking how the knowledge that fans bring to the game informs their experience of it. Others focus on the design of the game: for example the handling of narrative and its temporal dimensions, the articulation of core themes into ludic form, or the representational and aural strategies used by the game.
Book
The Blockchain Folk Theorem
Blockchains are distributed ledgers, operated within peer-to-peer networks. We model the proof-of-work blockchain protocol as a stochastic game and analyze the equilibrium strategies of rational, strategic miners. Mining the longest chain is a Markov perfect equilibrium, without forking, in line with Nakamoto (2008). The blockchain protocol, however, is a coordination game, with multiple equilibria. There exist equilibria with forks, leading to orphaned blocks and persistent divergence between chains. We also show how forks can be generated by information delays and software upgrades. Last we identify negative externalities implying that equilibrium investment in computing capacity is excessive.
Journal Article
Identification and Estimation of Dynamic Games When Players’ Beliefs Are Not in Equilibrium
This article deals with the identification and estimation of dynamic games when players’ beliefs about other players’ actions are biased, that is, beliefs do not represent the probability distribution of the actual behaviour of other players conditional on the information available. First, we show that an exclusion restriction, typically used to identify empirical games, provides testable non-parametric restrictions of the null hypothesis of equilibrium beliefs in dynamic games with either finite or infinite horizon. We use this result to construct a simple Likelihood Ratio test of equilibrium beliefs. Second, we prove that this exclusion restriction, together with consistent estimates of beliefs at two points in the support of the variable involved in the exclusion restriction, is sufficient for non-parametric point-identification of players’ belief functions as well as useful functions of payoffs. Third, we propose a simple two-step estimation method. We illustrate our model and methods using both Monte Carlo experiments and an empirical application of a dynamic game of store location by retail chains. The key conditions for the identification of beliefs and payoffs in our application are the following: (1) the previous year’s network of stores of the competitor does not have a direct effect on the profit of a firm, but the firm’s own network of stores at previous year does affect its profit because the existence of sunk entry costs and economies of density in these costs; and (2) firms’ beliefs are unbiased in those markets that are close, in a geographic sense, to the opponent’s network of stores, though beliefs are unrestricted, and potentially biased, for unexplored markets which are farther away from the competitors’ network. Our estimates show significant evidence of biased beliefs. Furthermore, imposing the restriction of unbiased beliefs generates a substantial attenuation bias in the estimate of competition effects.
Journal Article
On the Determinants of Cooperation in Infinitely Repeated Games
A growing experimental literature studies the determinants of cooperation in infinitely repeated games, tests different predictions of the theory, and suggests an empirical solution to the problem of multiple equilibria. To provide a robust description of the literature’s findings, we gather and analyze a metadata set of experiments on infinitely repeated prisoner’s dilemma games. The experimental data show that cooperation is affected by infinite repetition and is more likely to arise when it can be supported in equilibrium. However, the fact that cooperation can be supported in equilibrium does not imply that most subjects will cooperate. High cooperation rates will emerge only when the parameters of the repeated game are such that cooperation is very robust to strategic uncertainty. We also review the results regarding the effect of imperfect monitoring, changing partners, and personal characteristics on cooperation and the strategies used to support it.
Journal Article
Malleable Lies: Communication and Cooperation in a High Stakes TV Game Show
We investigate the credibility of nonbinding preplay statements about cooperative behavior, using data from a high-stakes TV game show in which contestants play a variant on the classic Prisoner’s Dilemma. We depart from the conventional binary approach of classifying statements as promises or not, and propose a more fine-grained two-by-two typology inspired by the idea that lying aversion leads defectors to prefer statements that are malleable to ex-post interpretation as truths. Our empirical analysis shows that statements that carry an element of conditionality or implicitness are associated with a lower likelihood of cooperation, and confirms that malleability is a good criterion for judging the credibility of cheap talk.
This paper was accepted by Elke Weber, judgment and decision making.
Journal Article
Dynamic Pricing of Perishable Assets Under Competition
We study dynamic price competition in an oligopolistic market with a
mix
of substitutable and complementary perishable assets. Each firm has a fixed initial stock of items and competes in setting prices to sell them over a finite sales horizon. Customers sequentially arrive at the market, make a purchase choice, and then leave immediately with some likelihood of no purchase. The purchase likelihood depends on the time of purchase, product attributes, and current prices. The demand structure includes time-variant linear and multinomial logit demand models as special cases. Assuming deterministic customer arrival rates, we show that any equilibrium strategy has a simple structure, involving a finite set of
shadow prices
measuring capacity externalities that firms exert on each other: equilibrium prices can be solved from a one-shot price competition game under the
current-time
demand structure, taking into account capacity externalities through the
time-invariant
shadow prices. The former reflects the transient demand side at every moment, and the latter captures the aggregate supply constraints over the sales horizon. This simple structure sheds light on dynamic revenue management problems under competition, which helps capture the essence of the problems under demand uncertainty. We show that the equilibrium solutions from the deterministic game provide precommitted and contingent heuristic policies that are asymptotic equilibria for its stochastic counterpart, when demand and supply are sufficiently large.
This paper was accepted by Yossi Aviv, operations management
.
Journal Article
On Synchronous, Asynchronous, and Randomized Best-Response Schemes for Stochastic Nash Games
In this paper, we consider a stochastic Nash game in which each player minimizes a parameterized expectation-valued convex objective function. In deterministic regimes, proximal best-response (BR) schemes have been shown to be convergent under a suitable spectral property associated with the proximal BR map. However, a direct application of this scheme to stochastic settings requires obtaining exact solutions to stochastic optimization problems at each iteration. Instead, we propose an
inexact
generalization of this scheme in which an inexact solution to the BR problem is computed in an expected-value sense via a stochastic approximation (SA) scheme. On the basis of this framework, we present three inexact BR schemes: (i) First, we propose a synchronous inexact BR scheme where all players simultaneously update their strategies. (ii) Second, we extend this to a randomized setting where a subset of players is randomly chosen to update their strategies while the other players keep their strategies invariant. (iii) Third, we propose an asynchronous scheme, where each player chooses its update frequency while using outdated rival-specific data in updating its strategy. Under a suitable contractive property on the proximal BR map, we proceed to derive almost sure convergence of the iterates to the Nash equilibrium (NE) for (i) and (ii) and mean convergence for (i)–(iii). In addition, we show that for (i)–(iii), the generated iterates converge to the unique equilibrium in mean at a linear rate with a prescribed constant rather than a sublinear rate. Finally, we establish the overall iteration complexity of the scheme in terms of projected stochastic gradient (SG) steps for computing an
ɛ
-NE
2
(or
ɛ
-NE
∞
) and note that in all settings, the iteration complexity is
O
(
1
/
ɛ
2
(
1
+
c
)
+
δ
)
, where
c
=
0
in the context of (i), and
c
> 0 represents the positive cost of randomization in (ii) and asynchronicity and delay in (iii). Notably, in the synchronous regime, we achieve a near-optimal rate from the standpoint of solving stochastic convex optimization problems by SA schemes. The schemes are further extended to settings where players solve two-stage stochastic Nash games with linear and quadratic recourse. Finally, preliminary numerics developed on a multiportfolio investment problem and a two-stage capacity expansion game support the rate and complexity statements.
Journal Article
Cognitive ability, character skills, and learning to play equilibrium
We investigate how cognitive ability and character skills influence the evolution of play toward Nash equilibrium in repeated strategic interactions. We find that more cognitively able subjects choose numbers closer to equilibrium, earn more, and converge more frequently to equilibrium play. We estimate a structural model of learning based on level k reasoning and find a positive relationship between cognitive ability and levels. Furthermore, the average level of more cognitively able subjects responds positively to the cognitive ability of their opponents. More agreeable and emotionally stable subjects also learn faster, although the effect of cognitive ability is stronger than that of personality.
Journal Article