Contest functions (alternatively, contest success functions) determine probabilities of winning and losing as a function of contestants' effort. They are used widely in many areas of economics that employ contest games, from tournaments and rent-seeking to conflict and sports. We first examine the theoretical foundations of contest functions and classify them into four types of derivation: stochastic, axiomatic, optimally-derived, and microfounded. The additive form (which includes the ratio or "Tullock" functional form) can be derived in all four different ways. We also explore issues in the econometric estimation of contest functions, including concerns with data, endogeneity, and model comparison.

We examine how the probability of persuading an audience depends on resources expended by contending parties as well as on other factors. We use a Bayesian approach whereby the audience makes inferences solely based on the evidence produced by the contestants. We find conditions that yield the well-known additive contest success function, including the logit function. We also find conditions that produce a generalized "difference" functional form. In all cases, there are three main determinants of audience choice: (i) the truth and other objective parameters of the environment; (ii) the biases of the audience, and (iii) the resources expended by the interested parties.

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D72, H57, K40, L10, Corruption, Deterrence, Media, Governance,

Over the past two millennia successful pre-modern states in Eurasia adopted and cultivated Big-God religions that emphasize (i) the ruler's legitimacy as divinely ordained and (ii) a morality adapted for large-scale societies that can have positive economic effects. We make sense of this development by building on previous research that has conceptualized pre-modern states as maximizing the ruler's profit. We model the interaction of rulers and subjects who have both material and psychological payoffs, the latter emanating from religious identity. Overall, religion reduces the cost of controlling subjects through the threat of violence, increases production, increases tax revenue, and reduces banditry. A Big-God ruler, who is also a believer, has greater incentives to invest in expanding the number of believers and the intensity of belief, as well as investing in state capacity. Furthermore, such investments are often complementary, mutually reinforcing one another, thus leading to an evolutionary advantage of rulers that adopted Big-God religions.