We Consider A Sequential Move Game In Which An Entrant Is Co

We Consider A Sequential Move Game In Which An Entrant Is Considering

We consider a sequential-move game in which an entrant is considering entering an industry in competition with an incumbent firm. The game involves strategic decisions made by both players over time, with the entrant contemplating whether to enter or stay out, and the incumbent deciding how to respond to potential entry. The primary analytical approach involves applying the Froeb rule of "look ahead and reason back," which entails backward induction to determine the strategic equilibrium of the game.

In analyzing such a game, it is essential to understand the payoffs associated with each strategic move and to identify the subgame perfect Nash equilibrium (SPNE). The entrant's success hinges on its ability to appropriately anticipate the incumbent's responses and to choose an optimal strategy that maximizes its payoff. If the entrant enters, it must consider whether the incumbent will accommodate or fight to deter entry, which could involve aggressive pricing, capacity expansion, or other retaliatory tactics.

Conversely, the incumbent's control over the game depends on its ability to influence the entrant's decision through strategic commitments, such as preemptive actions to create entry barriers or by signaling that entry would be unprofitable. The incumbent can leverage the game structure to maintain control by convincing the entrant that entry would lead to negative payoffs, thereby deterring entry altogether.

The Nash equilibrium in this context refers to a set of strategies for both players where neither has an incentive to unilaterally deviate. This equilibrium can manifest as a scenario where the entrant chooses to stay out because the expected payoff from entry is negative, given the incumbent's responses, and the incumbent chooses to fight or accommodate based on the expected profitability of each response. The classic duopoly models, such as Cournot competition, provide foundational insights into how firms strategically set quantities or prices over time and how equilibrium outcomes depend on the strategic interactions of the players.

Applying the insight from Cournot and other oligopoly models, the outcome of the sequential game depends critically on cost structures, market demand, and strategic capabilities. For example, if the incumbent can commit to aggressive pricing strategies or capacity expansions, it can effectively deter entry, resulting in a player in control of the game. Alternatively, if the entrant possesses cost advantages or innovative product offerings, it may succeed in entering despite incumbent opposition.

In conclusion, the success of the entrant depends on its ability to accurately forecast the incumbent's strategic responses and to commit to actions that tip the strategic balance. The incumbent can maintain control through credible commitments and strategic signaling. The game theoretical solution, represented as the subgame perfect Nash equilibrium, reflects these strategic considerations and provides insights into the likely outcome of the entry decision and market competition.

Paper For Above instruction

Sequential move games in oligopoly and entry deterrence are central to understanding strategic interactions between incumbents and potential entrants in an industry. These models exemplify how firms anticipate each other's moves and make strategic decisions over time, employing concepts like backward induction and subgame perfect Nash equilibrium (SPNE). Analyzing such a game involves examining the incentives and potential payoffs for both the entrant and the incumbent, considering their strategic capabilities, costs, and market conditions.

In a typical framework, the entrant must decide whether to enter the market by considering the incumbent's response strategies. If the entrant chooses to enter, it faces the threat of retaliation or aggressive actions from the incumbent, which might include price cuts, capacity expansion, or legal barriers. The incumbent, in turn, can choose to fight or accommodate, depending on which response maximizes its profitability. The strategic decision-making process thus revolves around the credibility of threats and promises, which are crucial in determining the equilibrium outcome.

The "look ahead and reason back" principle from Froeb emphasizes the importance of backward reasoning in game analysis. Starting from the last moves of the game, both players consider what the other would do in response to their actions. This iterative reasoning helps identify equilibrium strategies that are credible and stable. For instance, the incumbent might signal a willingness to fight to deter entry, but if such a strategy is unprofitable, the equilibrium would involve the incumbent ceding or strategically bluffing.

The concept of control in this game is linked to the strategic ability of one player to influence or predetermine the outcome. The incumbent can be in control if it can credibly commit to a response that makes entry unprofitable, thus deterring the entrant. This control manifests through investments, contractual commitments, or signaling tactics that influence the entrant’s expectations and decisions. On the other hand, if the entrant has low costs or alternative advantages, it may succeed in entering despite the incumbent's efforts.

The Nash equilibrium in this context typically corresponds to a set of strategies where neither player benefits from unilateral deviations. It often results in an outcome where the entrant either enters and fights or stays out based on the perceived profitability, and the incumbent decides whether to fight or accommodate accordingly. Classical duopoly models, especially Cournot and Bertrand variants, highlight how strategic interactions influence equilibrium prices and quantities over time, and how these outcomes depend heavily on the timing of moves and the strategic capabilities of the firms.

For example, in a Cournot-based sequential game, the incumbent might commit to a certain quantity first, thereby influencing the entrant's best response. Conversely, the entrant's entry can be preempted through strategic capacity investments or pricing strategies that increase the cost of entry or the potential retaliation costs. Both firms consider these strategic trade-offs, with equilibrium outcomes reflecting a balance of competitive and strategic considerations.

Overall, the success of an entrant in such a sequential game hinges on its ability to accurately anticipate incumbent responses and strategically commit to an entry or non-entry decision. The incumbent maintains control through credible threats and strategic commitments that shape the entrant's expectations. These interactions are elegantly captured by the SPNE, which models the strategic reasoning throughout the game and predicts the likely market outcome based on the strategic equilibrium point.

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