Uniqueness of equilibrium in two-player asymmetric Tullock contests with intermediate discriminatory power

Feng, Xin; Lu, Jingfeng

doi:10.1016/j.econlet.2017.07.017

Cited by 23 publications

(8 citation statements)

References 19 publications

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“…Second, if r k < r ≤ 2, i.e., for an intermediate discriminatory power, the Nash equilibrium is unique and in semimixed strategies in which only one player pursues a pure strategy, while the other randomizes (Ewerhart, 2017b;Feng & Lu, 2017;Wang, 2010). These studies imply that, for i, j ∈ {A, B} with i ≠ j and w k…”

Section: The Tournament and The Matchesmentioning

confidence: 99%

“…Second, if

r_{k} < r \leq 2

, i.e., for an intermediate discriminatory power, the Nash equilibrium is unique and in semimixed strategies in which only one player pursues a pure strategy, while the other randomizes (Ewerhart, ; Feng & Lu, ; Wang, ). These studies imply that, for

i, j \in {A, B}

with

i \neq j

and

w_{i}^{k} - ℓ_{i}^{k} = min false{w_{A}^{k} - ℓ_{A}^{k}, w_{B}^{k} - ℓ_{B}^{k} false}

, the equilibrium (expected) efforts are

E (x_{i}^{k}) = \frac{1}{r} {(r - 1)}^{\frac{r - 1}{r}} \frac{{(w_{i}^{k} - ℓ_{i}^{k})}^{2}}{w_{j}^{k} - ℓ_{j}^{k}} and x_{j}^{k} = \frac{1}{r} {(r - 1)}^{\frac{r - 1}{r}} (w_{i}^{k} - ℓ_{i}^{k}),

the equilibrium winning probabilities are

p_{i}^{k} = \frac{1}{r} {(r - 1)}^{\frac{r - 1}{r}} \frac{w_{i}^{k} - ℓ_{i}^{k}}{w_{j}^{k} - ℓ_{j}^{k}} and p_{j}^{k} = 1 - p_{i}^{k},

and the expected equilibrium payoffs are

E_{i}^{k} = ℓ_{i}^{k}

…”

Section: The Tournament and The Matchesmentioning

confidence: 99%

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Are sequential round‐robin tournaments discriminatory?

Sahm

2018

J Public Economic Theory

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Abstract I examine sequential round-robin tournaments with three and four symmetric players. Each player is matched once with each other player. If the matches are organized as Tullock contests (all-pay auctions), the tournament will be almost fair (highly discriminatory): subject to the position of their matches in the sequence of the tournament, the differences in players' ex-ante winning probabilities and expected payoffs will be small (large). The differing results originate from the higher discriminating power of the all-pay auction. Moreover, the resulting discouragement effect in tournaments with all-pay auctions implies lower aggregate effort than in tournaments with suitable Tullock contests. The fairness of round-robin tournaments may be improved by the use of an endogenous sequence of matches or the requirement that players fix their effort ex-ante. Terms of use: Documents in

show abstract

Section: The Tournament and The Matchesmentioning

confidence: 99%

“…Second, if

r_{k} < r \leq 2

i, j \in {A, B}

with

i \neq j

and

w_{i}^{k} - ℓ_{i}^{k} = min false{w_{A}^{k} - ℓ_{A}^{k}, w_{B}^{k} - ℓ_{B}^{k} false}

, the equilibrium (expected) efforts are

E (x_{i}^{k}) = \frac{1}{r} {(r - 1)}^{\frac{r - 1}{r}} \frac{{(w_{i}^{k} - ℓ_{i}^{k})}^{2}}{w_{j}^{k} - ℓ_{j}^{k}} and x_{j}^{k} = \frac{1}{r} {(r - 1)}^{\frac{r - 1}{r}} (w_{i}^{k} - ℓ_{i}^{k}),

the equilibrium winning probabilities are

p_{i}^{k} = \frac{1}{r} {(r - 1)}^{\frac{r - 1}{r}} \frac{w_{i}^{k} - ℓ_{i}^{k}}{w_{j}^{k} - ℓ_{j}^{k}} and p_{j}^{k} = 1 - p_{i}^{k},

and the expected equilibrium payoffs are

E_{i}^{k} = ℓ_{i}^{k}

…”

Section: The Tournament and The Matchesmentioning

confidence: 99%

Are sequential round‐robin tournaments discriminatory?

Sahm

2018

J Public Economic Theory

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“…While there are many types of ATP and WTA tournaments-such as ATP 1000, ATP 500, etc.-the theoretical and empirical implications of these differences are left to future research. from the fact that payoff functions are globally concave in player's own effort given the other's strategy (Feng & Lu, 2017). 2.…”

Section: Discussionmentioning

confidence: 99%

“…However, uniqueness has been established for many types of Tullock contests. For example, if the winning probability is given by a x 1 r a x 1 r + x 2 r where r ≤ 1 and x 1 , x 2 are effort levels for player 1 and player 2, respectively, then uniqueness immediately follows from the fact that payoff functions are globally concave in player’s own effort given the other’s strategy (Feng & Lu, 2017).…”

mentioning

confidence: 99%

Set-level Strategic and Psychological Momentum in Best-of-three-set Professional Tennis Matches

Depken

Gandar²,

Shapiro

2022

Journal of Sports Economics

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We provide a theoretical and empirical analysis of strategic momentum and psychological momentum in best-of-three contests between players with unequal skills. As a theoretical benchmark, we develop a fully rational model of best-of-three contests and define psychological momentum as systematic deviation from the theoretical equilibrium. An empirical analysis of 66,262 professional tennis matches from 2002 to 2020 shows that our theoretical model closely matches first set outcomes, which is when set-level psychological momentum is absent. Overall, the empirical results show that both strategic momentum and psychological momentum contribute to the outcomes of best-of-three tennis contests.

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“…However, they did not characterize equilibria for smooth distributions of noise. 8 Ewerhart (2017) and Feng and Lu (2017) characterized the semi-mixed equilibrium in Tullock contests. This type of equilibrium corresponds to the insurgency case studied below.…”

Section: Introductionmentioning

confidence: 99%

A Typology of Military Conflict Based on the Hirshleifer Contest

Ewerhart

2021

SSRN Journal

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Uniqueness of equilibrium in two-player asymmetric Tullock contests with intermediate discriminatory power

Cited by 23 publications

References 19 publications

Are sequential round‐robin tournaments discriminatory?

Are sequential round‐robin tournaments discriminatory?

Set-level Strategic and Psychological Momentum in Best-of-three-set Professional Tennis Matches

A Typology of Military Conflict Based on the Hirshleifer Contest

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