Price of Anarchy in Bernoulli Congestion Games with Affine Costs

We consider an atomic congestion game in which each player participates in the game with an exogenous and known probability $p_{i}\in[0,1]$, independently of everybody else, or stays out and incurs no cost. We first prove that the resulting game is potential. Then, we compute the parameterized price of anarchy to characterize the impact of demand uncertainty on the efficiency of selfish behavior. It turns out that the price of anarchy as a function of the maximum participation probability $p=\max_{i} p_{i}$ is a nondecreasing function. The worst case is attained when players have the same participation probabilities $p_{i}\equiv p$. For the case of affine costs, we provide an analytic expression for the parameterized price of anarchy as a function of $p$. This function is continuous on $(0,1]$, is equal to $4/3$ for $0<p\leq 1/4$, and increases towards $5/2$ when $p\to 1$. Our work can be interpreted as providing a continuous transition between the price of anarchy of nonatomic and atomic games, which are the extremes of the price of anarchy function we characterize. We show that these bounds are tight and are attained on routing games -- as opposed to general congestion games -- with purely linear costs (i.e., with no constant terms).Comment: 29 pages, 6 figure

Optimality of Winner-Take-All Contests: The Role of Attitudes toward Risk

It has been established in the literature that, under the assumption of risk-neutral contestants, it is usually optimal for an effort-maximizing contest organizer with a fixed prize budget to award everything to a single winner. This paper studies the role of risk attitudes – risk aversion and prudence in particular – in determining the optimality of winner-take-all contests. We compare the typical single-winner lottery contest with two alternative ways of spreading the rewards to more players: through holding multiple prize-giving lottery competitions or through guaranteeing a bottom prize for the losers. In the first comparison, we found that the multiple-competition contest is as effective as the winner-take-all contest when the contestants are risk neutral, but the former induces more effort than the latter when the contestants are both risk averse and prudent. In the second comparison, we found that the contest with a bottom prize is always dominated by the winner-take-all contest when the contestants are risk neutral, but the former could have an advantage over the latter when the contestants are both risk averse and prudent, and it is more likely so as the contestants become more prudent

Optimality of Winner-Take-All Contests: The Role of Attitudes toward Risk

It has been established in the literature that, under the assumption of risk-neutral contestants, it is usually optimal for an effort-maximizing contest organizer with a fixed prize budget to award everything to a single winner. This paper studies the role of risk attitudes – risk aversion and prudence in particular – in determining the optimality of winner-take-all contests. We compare the typical single-winner lottery contest with two alternative ways of spreading the rewards to more players: through holding multiple prize-giving lottery competitions or through guaranteeing a bottom prize for the losers. In the first comparison, we found that the multiple-competition contest is as effective as the winner-take-all contest when the contestants are risk neutral, but the former induces more effort than the latter when the contestants are both risk averse and prudent. In the second comparison, we found that the contest with a bottom prize is always dominated by the winner-take-all contest when the contestants are risk neutral, but the former could have an advantage over the latter when the contestants are both risk averse and prudent, and it is more likely so as the contestants become more prudent

La Crema: A case study of mutual fire insurance

We analyze a mutual fire insurance mechanism used in Andorra, which is called La Crema in the local language. This mechanism relies on households' announced property values to determine how much a household is reimbursed in the case of a fire and how payments are apportioned among other households. The only Pareto eficient allocation reachable through the mechanism requires that all households honestly report the true value of their property. However, such honest reporting is not an equilibrium except in the extreme case where the property values are identical for all households. Nevertheless, as the size of the society becomes large, the benefits from deviating from truthful reporting vanish, and all of the non-degenerate equilibria of the mechanism are nearly truthful and approximately Pareto efficient.Insurance, contract theory, mechanism design, truthful revelation

Risk-averse multi-armed bandits and game theory

The multi-armed bandit (MAB) and game theory literature is mainly focused on the expected cumulative reward and the expected payoffs in a game, respectively. In contrast, the rewards and the payoffs are often random variables whose expected values only capture a vague idea of the overall distribution. The focus of this dissertation is to study the fundamental limits of the existing bandits and game theory problems in a risk-averse framework and propose new ideas that address the shortcomings. The author believes that human beings are mostly risk-averse, so studying multi-armed bandits and game theory from the point of view of risk aversion, rather than expected reward/payoff, better captures reality. In this manner, a specific class of multi-armed bandits, called explore-then-commit bandits, and stochastic games are studied in this dissertation, which are based on the notion of Risk-Averse Best Action Decision with Incomplete Information (R-ABADI, Abadi is the maiden name of the author's mother). The goal of the classical multi-armed bandits is to exploit the arm with the maximum score defined as the expected value of the arm reward. Instead, we propose a new definition of score that is derived from the joint distribution of all arm rewards and captures the reward of an arm relative to those of all other arms. We use a similar idea for games and propose a risk-averse R-ABADI equilibrium in game theory that is possibly different from the Nash equilibrium. The payoff distributions are taken into account to derive the risk-averse equilibrium, while the expected payoffs are used to find the Nash equilibrium. The fundamental properties of games, e.g. pure and mixed risk-averse R-ABADI equilibrium and strict dominance, are studied in the new framework and the results are expanded to finite-time games. Furthermore, the stochastic congestion games are studied from a risk-averse perspective and three classes of equilibria are proposed for such games. It is shown by examples that the risk-averse behavior of travelers in a stochastic congestion game can improve the price of anarchy in Pigou and Braess networks. Furthermore, the Braess paradox does not occur to the extent proposed originally when travelers are risk-averse. We also study an online affinity scheduling problem with no prior knowledge of the task arrival rates and processing rates of different task types on different servers. We propose the Blind GB-PANDAS algorithm that utilizes an exploration-exploitation scheme to load balance incoming tasks on servers in an online fashion. We prove that Blind GB-PANDAS is throughput optimal, i.e. it stabilizes the system as long as the task arrival rates are inside the capacity region. The Blind GB-PANDAS algorithm is compared to FCFS, Max-Weight, and c-mu-rule algorithms in terms of average task completion time through simulations, where the same exploration-exploitation approach as Blind GB-PANDAS is used for Max-Weight and c-$\mu$-rule. The extensive simulations show that the Blind GB-PANDAS algorithm conspicuously outperforms the three other algorithms at high loads

Pricing and Investments in Internet Security: A Cyber-Insurance Perspective

Internet users such as individuals and organizations are subject to different types of epidemic risks such as worms, viruses, spams, and botnets. To reduce the probability of risk, an Internet user generally invests in traditional security mechanisms like anti-virus and anti-spam software, sometimes also known as self-defense mechanisms. However, such software does not completely eliminate risk. Recent works have considered the problem of residual risk elimination by proposing the idea of cyber-insurance. In this regard, an important research problem is the analysis of optimal user self-defense investments and cyber-insurance contracts under the Internet environment. In this paper, we investigate two problems and their relationship: 1) analyzing optimal self-defense investments in the Internet, under optimal cyber-insurance coverage, where optimality is an insurer objective and 2) designing optimal cyber-insurance contracts for Internet users, where a contract is a (premium, coverage) pair

Optimality of winner-take-all contests: the role of attitudes toward risk

This paper studies the role of risk attitudes in determining the optimality of winner-take-all contests. We compare the typical singlewinner lottery contest with two alternatives, both spreading the rewards to more players: through holding multiple prize-giving lottery competitions or through guaranteeing a bottom prize for the losers. In the first comparison, we find that the multiple-competition contest is as effective as the winner-take-all contest when the contestants are risk neutral, but the former induces more effort than the latter when the contestants are both risk averse and prudent. In the second comparison, we find that the contest with a bottom prize is always dominated by the winner-take-all contest when the contestants are risk neutral, but the former could have an advantage over the latter when the contestants are both risk averse and prudent, and it is more likely so as the contestants become more prudent

Pooling, Pricing and Trading of Risks

Abstract. Exchange of risks is considered here as a transferableutility, cooperative game, featuring risk averse players. Like in competitive equilibrium, a core solution is determined by shadow prices on state-dependent claims. And like in finance, no risk can properly be priced only in terms of its marginal distribution. Pricing rather depends on the pooled risk and on the convolution of individual preferences. The paper elaborates on these features, placing emphasis on the role of prices and incompleteness. Some novelties come by bringing questions about existence, computation and uniqueness of solutions to revolve around standard Lagrangian duality. Especially outlined is how repeated bilateral trade may bring about a price-supported core allocation.Keywords: cooperative game; transferable utility; core; risks; mutual insurance; contingent prices; bilateral exchange; supergradients; stochastic approximation.

Optimality of winner-take-all contests

This paper studies the role of risk attitudes in determining the optimality of winner-take-all contests. We compare the typical singlewinner lottery contest with two alternatives, both spreading the rewards tomore players: through holding multiple prize-giving lottery competitions or through guaranteeing a bottom prize for the losers. In the first comparison, we find that the multiple-competition contest is as effective as the winner-take-all contest when the contestants are risk neutral, but the former induces more effort than the latter when the contestants are both risk averse and prudent. In the second comparison, we find that the contest with a bottom prize is always dominated by the winner-take-all contest when the contestants are risk neutral, but the former could have an advantage over the latter when the contestants are both risk averse and prudent, and it is more likely so as the contestants become more prudent

Strategic Behavior and Underpricing in Uniform Price Auctions

We study uniform price auctions using a dataset which includes individual bidders' demand schedules in Finnish Treasury auctions during the period 1992-99. Average underpricing amounts to .041% of face value. Theory suggests that underpricing may result from monopsonistic market power. We develop and test robust implications from this theory and ¯nd that it has little support in the data. For example, bidders' individual demand functions do not respond to increased competition in the manner predicted by the theory. We also present evidence that the Finnish Treasury acts strategically, taking into account the fact that the auctions are part of a repeated game between the Treasury and the primary dealers. Empirically, the main driver behind bidder behavior and underpricing is the volatility of bond returns. Since there is no evidence that bidders are risk averse, this suggests that private information and the winner's curse may play an important role in these auctions.Multiunit auctions, uniform price auctions, treasury auctions, market power, demand functions, underpricing, supply uncertainty, seller behavior