This thesis focuses on contests and conflicts with heterogeneous participants where the asymmetries arise from players’ preferences, skills, or resource constraints. The work consists of two chapters. Each section proposes a theoretical framework and provides an empirical justification of the key patterns discovered. In the first chapter, I develop a model where two players with asymmetric preferences engage in a contest game. Prizes consist of two non-tradable divisible goods. I characterize the optimal prize allocation that maximizes aggregate effort of the contestants. When heterogeneity is severe, the designer benefits by giving a positive prize to the loser. This allocation eliminates the advantage of the stronger competitor and makes the contest homogeneous. As a consequence, the opponent has higher chances to win and exerts more effort in equilibrium. This positive response increases aggregate effort. The model mirrors the job promotion setting with monetary and non-monetary rewards. Using data from first-round matches of two professional tennis competitions where prizes include money and the ATP ranking points (career concerns), I structurally estimate contestants’ skills and preferences. Overlooking multi-dimensionality results in biased estimates of the prize incentive effects. Counterfactual experiments show that reallocating 5% of money and 2% of the ATP ranking points from final winning prizes to first-round losing rewards could improve expected aggregate effort in relatively heterogeneous matches by more than 4.9%. The second chapter, jointly written with Madina Kurmangaliyeva, adopts the contest setting to study main determinants of “victim-defendant” settlements. This institute is widely used in both civil and criminal legal practices. Understanding how the power imbalance affects the negotiation process is crucial for the optimal design of the justice system. We develop a theoretical model where the victim (she) and the defendant (he) must exert costly effort for the case to reach / avoid the court. Before the game starts, the defendant can settle with the victim by making her a 'take-it-or-leave-it' offer. Improving the defendant’s bargaining position reduces the settlement amount. When the victim has strong preferences for revenge, the agreement may fail to happen even if the defendant can afford the optimal offer. Using the data on criminal traffic offenses in Russia for 2013–2014 (56’000 complete cases), we structurally estimate the model and recover individual preferences and fighting abilities. Overall, defendants are 10 times wealthier than their victims. Offenders who manage to settle face significantly less disutility than their peers going to court (–.007 against –810.78 for 'car vs. pedestrian' accidents). Thus, 'victim-defendant' settlements can rise the inequality before the law. If Russia abandoned the given institute, the prison population could increase by 2’850 inmates, which would cost the state e2.3 million per year.