This thesis investigates different aspects of competition under uncertainty using the tools of game theory. In Chapter 1, I consider a quantity oligopoly game. One of the firms is presented with an opportunity to commit to some output before the demand becomes known, but may add to it afterwards, then moving simultaneously with the rivals. I show that the more cost-efficient firm is more likely to behave like a Stackelberg leader, i.e. to produce the optimal Stackelberg leader quantity ex-ante and refrain from adding to it later, letting the rivals respond to its ex-ante output in the manner of Stackelberg followers.In Chapter 2, I study a model of an electoral contest. Two symmetric parties allocate their endowments to building platforms on various issues before the start of a campaign. Next, one of the issues becomes decisive in the course of the campaign with a commonly known probability. The outcome of the election depends on the difference in competence in this issue. I show that if the payoff functions are convex in this difference-the case of 'increasing returns to power'-parties differentiate each other by selecting different campaign issues. On the contrary, when the payoff functions are concave in this difference-the case of 'decreasing returns to power'-parties mimic each other by investing the same amounts into the same issues. Thus, incentives for selecting campaign issues depend critically on the shape of the payoff functions, which might be determined by (1) a non-linear technology transforming parties' investment in various topics into voters' perception of their competence, (2) or parties' inherent motivation for winning by a big margin due to parties' ideological convictions or rent-seeking, (3) or an electoral system giving winners or big parties a disproportionate advantage in the assigned number of seats, (4) or a relatively high extent of power given to the winning party once in office.