This paper presents a tractable model to study the effect of immigration on host countries’ school system and student outcomes. In our model, education quality and student outcomes are determined endogenously by the interaction of parents, schools and policy-makers deciding educational resources. Immigration decisions are based on economic factors, immigration policy, as well as on “parental motivation” (parents’ concerns about their children education achievement). The model yields results that are consistent with central empirical regularities of the school effects of immigration: (1) there is a negative effect of immigrant pupils on native students; (2) the increasing shares of immigrant students are associated with the decline of school resources and quality; (3) the school performance of immigrant children is positively associated with immigration costs; and (4) school achievement increases in parental motivation and those immigrant children with highly motivated parents tend to outperform native children. Importantly, our analysis clarifies under which conditions these empirical regularities take place and emphasizes that the effect of immigration on native pupils is mediated by the way the school system reacts to changes in class composition.

We investigate a version of the classic Colonel Blotto game in which individual battlefields may have different values. Two players allocate a fixed discrete budget across battlefields. Each battlefield is won by the player who allocates the most to that battlefield. The player who wins the battlefields with highest total value receives a constant winner payoff, while the other player receives a constant loser payoff. We focus on apex games, in which there is one large and several small battlefields. A player wins if he wins the large and any one small battlefield, or all the small battlefields. For each of the games we study, we compute an equilibrium and we show that certain properties of equilibrium play are the same in any equilibrium. In particular, the expected share of the budget allocated to the large battlefield exceeds its value relative to the total value of all battlefields, and with a high probability (exceeding 90\% in our treatments) resources are spread over more battlefields than are needed to win the game. In a laboratory experiment, we find that strategies that spread resources widely are played frequently, consistent with equilibrium predictions. In the treatment where the asymmetry between battlefields is strongest, we also find that the large battlefield receives on average more than a proportional share of resources. In a control treatment, all battlefields have the same value and our findings are consistent with previous experimental findings on Colonel Blotto games.