Optimal Risk Taking in an Uneven Tournament Game with Risk Averse Players

We analyze the optimal choice of risk in a two-stage tournament game between two players that have different concave utility functions. At the first stage, both players simultaneously choose risk. At the second stage, both observe overall risk and simultaneously decide on effort or investment. The results show that those two effects which mainly determine risk taking — an effort effect and a likelihood effect — are strictly interrelated. This finding sharply contrasts with existing results on risk taking in tournament games with symmetric equilibrium efforts where such linkage can never arise. Hence, previous findings based on symmetry at the effort stage turn out to be nongeneric

Optimal Seedings in Elimination Tournaments

We study an elimination tournament with heterogenous contestants whose ability is common-knowledge. Each pair-wise match is modeled as an all-pay auction where the winner gets the right to compete at the next round. Equilibrium efforts are in mixed strategies, yielding rather complex play dynamics: the endogenous win probabilities in each match depend on the outcome of other matches through the identity of the expected opponent in the next round. The designer can seed the competitors according to their ranks. For tournaments with four players we find optimal seedings with respect to three different criteria: 1) maximization of total effort in the tournament; 2) maximization of the probability of a final among the two top ranked teams; 3) maximization of the win probability for the top player. In addition, we find the seedings ensuring that higher ranked players have a higher probability to win the tournament. Finally, we compare the theoretical predictions with data from NCAA basketball tournaments

Deterrence in Rank-Order Tournaments

In a tournament, competitors may engage in undesirable activities, or 'cheating', in order to gain an advantage. Examples of such activities include the taking of steroids, plagiarism, and 'creative accounting'. This paper considers the problem of deterrence of these activities and finds that there exist special considerations that are not present in a traditional model of law enforcement. For example, an agent's returns to cheating depend on the cheating decisions of others, and so there may exist multiple equilibria. The problem of multiple equilibria can be reduced when the first-place prize is awarded to the person that performed best without cheating. Moreover, we show that re-awarding prizes reduces the amount of monitoring required to ensure compliance. We also demonstrate that monitoring costs can be further reduced by monitoring the winner of the tournament more than the loser, and by manipulating prizes, including through the introduction of prizes for non-winners.Enforcement; Cheating; Tournament

Statistical Feature Combination for the Evaluation of Game Positions

This article describes an application of three well-known statistical methods in the field of game-tree search: using a large number of classified Othello positions, feature weights for evaluation functions with a game-phase-independent meaning are estimated by means of logistic regression, Fisher's linear discriminant, and the quadratic discriminant function for normally distributed features. Thereafter, the playing strengths are compared by means of tournaments between the resulting versions of a world-class Othello program. In this application, logistic regression - which is used here for the first time in the context of game playing - leads to better results than the other approaches.Comment: See http://www.jair.org/ for any accompanying file

We haven't got a seat on the bus for you or All the seats are mine: Narratives and career transitions in professional golf

In this article we explore how the stories an athlete tells throughout life in sport affect her career transition experiences. We base our enquiry on a social constructionist conception of narrative theory which holds that storytelling is integral to the creation and maintenance of identity and sense of self. Life stories were gathered through interviews with two professional women golfers (Christiana and Kandy) over a six‐year period. Through a narrative analysis of structure and form we explored each participant’s stories of living in and withdrawing from professional golf. We suggest Christiana told monological performance‐oriented stories which, while aligning with the culture of elite sport, resulted in an exclusive athletic identity and foreclosure of alternative selves and roles. On withdrawal, Christiana experienced narrative wreckage, identity collapse, mental health difficulties and considerable psychological trauma. In contrast, Kandy told dialogical discovery‐oriented stories which, while being in tension with the dominant performance narrative, created and sustained a multidimensional identity and self. Her stories and identity remained intact, authentic and continuous on withdrawal from tournament golf and she experienced few psychological problems

Approximately Strategyproof Tournament Rules: On Large Manipulating Sets and Cover-Consistence

We consider the manipulability of tournament rules, in which n teams play a round robin tournament and a winner is (possibly randomly) selected based on the outcome of all binom{n}{2} matches. Prior work defines a tournament rule to be k-SNM-? if no set of ? k teams can fix the ? binom{k}{2} matches among them to increase their probability of winning by >? and asks: for each k, what is the minimum ?(k) such that a Condorcet-consistent (i.e. always selects a Condorcet winner when one exists) k-SNM-?(k) tournament rule exists? A simple example witnesses that ?(k) ? (k-1)/(2k-1) for all k, and [Jon Schneider et al., 2017] conjectures that this is tight (and prove it is tight for k=2). Our first result refutes this conjecture: there exists a sufficiently large k such that no Condorcet-consistent tournament rule is k-SNM-1/2. Our second result leverages similar machinery to design a new tournament rule which is k-SNM-2/3 for all k (and this is the first tournament rule which is k-SNM-(<1) for all k). Our final result extends prior work, which proves that single-elimination bracket with random seeding is 2-SNM-1/3 [Jon Schneider et al., 2017], in a different direction by seeking a stronger notion of fairness than Condorcet-consistence. We design a new tournament rule, which we call Randomized-King-of-the-Hill, which is 2-SNM-1/3 and cover-consistent (the winner is an uncovered team with probability 1)

Abandoning the performance narrative: Two women's stories of transition from professional sport

Despite its potential to illuminate psychological processes within socio-cultural contexts, examples of narrative research are rare in sport psychology. In this study, we employed an analysis of narrative to explore two women's stories of living in, and withdrawing from, professional tournament golf gathered through life history interviews conducted over 6 years. Our findings suggest that immersion in elite sport culture shaped these women's identities around performance values of single-minded dedication to sport and prioritization of winning above all other areas of life. When the performance narrative ceased to "fit" their changing lives, both women, having no alternative narrative to guide their personal life stories, experienced narrative wreckage and considerable personal trauma. They required asylum-a place of refuge where performance values were no longer paramount-to story their lives around a relational narrative that reinstated a coherent identity while providing meaning and worth to life after golf. © Association for Applied Sport Psychology