In The Text, We Considered A Sequential Move Game
In The Text We Considered A Sequential Move Game In Which An Entrant
In the given scenario, we analyze a sequential-move game where an entrant considers entering an industry already occupied by an incumbent firm. The game involves strategic decisions by the entrant, who can choose to stay or withdraw if the incumbent fights the entry attempt. The payoff structure is revised to incorporate the possibility of withdrawal and its associated consequences, and the objective is to determine the game’s equilibrium and assess whether the entrant benefits from having the option to withdraw.
The original game, as presented in the referenced text, involves an entrant contemplating entry into an industry with the incumbent’s reaction influencing the outcome. Typically, in such models, the entrant’s decision to enter depends on the anticipated response from the incumbent, who may fight or accommodate. The strategic interplay is often represented as a sequential game, where the entrant makes an initial move (entry or stay out), and the incumbent responds accordingly.
In the modified game scenario, the entrant faces additional strategic options once entry is attempted. Specifically, if the incumbent chooses to fight, the entrant can choose to withdraw or stay, each with specific payoffs and consequences. These options profoundly influence the equilibrium analysis. The payoffs are summarized as follows:
- If the entrant withdraws after being fought: The entrant incurs a loss of 1, and the incumbent gains 8.
- If the entrant stays after being fought: Both the entrant and the incumbent incur a loss of 5 each.
Analyzing this model involves constructing a payoff matrix or game tree that captures these choices and payoffs. By applying backward induction, we can identify subgame perfect equilibrium strategies.
Step 1: Incumbent’s decision to fight or accommodate
If the entrant chooses to enter, the incumbent responds with either to fight or to accommodate:
- If the incumbent fights:
- The entrant’s decision: withdraw or stay.
- If the entrant withdraws: payoff to the entrant = -1, incumbents = 8.
- If the entrant stays: payoff to the entrant = -5, incumbents = -5.
- If the incumbent accommodates, the payoffs (not specified here but typically positive for both or as per prior models) are relevant; however, since we're focused on fighting scenarios, we predominantly analyze the fight branch.
Step 2: Entrant’s decision after being fought
Given the payoffs:
- Withdraw: -1 for the entrant.
- Stay: -5 for the entrant.
The entrant, facing these payoffs, would prefer to withdraw when fought, as -1 is better than -5.
Step 3: Incumbent’s decision to fight
Knowing the entrant will prefer to withdraw if fought, the incumbent’s decision depends on whether fighting yields sufficiently high payoff (8) when the entrant withdraws. Since the payoff when fighting and the entrant withdraws is 8, this is highly attractive to the incumbent.
Conclusion: Equilibrium analysis
Given these payoff structures, the subgame perfect equilibrium involves:
- The entrant deciding whether to attempt entry, anticipating that if the incumbent fights, the entrant will withdraw due to the better payoff (-1 versus -5).
- The incumbent choosing to fight, knowing that it induces the entrant to withdraw, thereby securing a payoff of 8.
Therefore, the equilibrium involves:
- Entry by the entrant, followed by the incumbent fighting.
- The entrant withdrawing when fought, accepting the small loss.
- The incumbent fighting, securing the payoff of 8.
If the entrant had no option to withdraw, the payoffs in case of fighting could be different, potentially leading to different strategic considerations. The ability to withdraw effectively deters the incumbent from fighting, as the entrant can preempt costly conflicts and minimize losses.
Is the entrant better off with or without the ability to withdraw?
Having the ability to withdraw enhances the entrant’s strategic position. The threat of withdrawal discourages the incumbent from fighting aggressively because the incumbent’s payoff (8) is higher than the payoff if the entrant stays and both suffer losses (-5 each). Without withdrawal options, the entrant might be forced to endure fighting costs or avoid entry altogether, potentially resulting in no entry or inefficient outcomes. With withdrawal rights, the entrant can credibly threaten to exit, leading to more favorable equilibrium outcomes where entry can be successful and the incumbent is deterred from costly fights.
Conclusion:
The equilibrium of the game, considering the withdrawal option, involves the entrant entering and then withdrawing if fought, prompting the incumbent to abstain from fighting. This strategic advantage suggests that the entrant is better off with the ability to withdraw, as it influences incumbent behavior favorably and reduces potential losses. The withdrawal option acts as a credible threat, enhancing the entrant’s bargaining power and resulting in more efficient and less costly strategic interactions.
Paper For Above instruction
The analysis of sequential move games in industrial organization provides valuable insights into strategic decision-making processes between entrants and incumbents. In the classical models discussed in economic literature, firms’ entry and competitive responses are analyzed through game-theoretic lenses, often assuming that entrants have limited strategic options once the initial decision to enter is made. However, expanding these models to incorporate an entrant’s ability to withdraw presents a richer, more realistic framework that captures real-world strategic behavior more accurately.
In the basic entry game, a new entrant deciding whether to enter a market faces the incumbent’s potential responses: fighting or accommodating. The incumbent’s decision is typically based on maximizing profits, balancing the costs of fighting (e.g., price wars, advertising battles, or increased R&D) against the benefits of deterring entry and maintaining market share. The entrant, anticipating this response, uses backward induction to strategize, aiming to choose entry if the expected payoff outweighs abstention.
Introducing the option to withdraw after being fought adds a strategic layer that enhances the equilibrium analysis. When fighting occurs, the entrant can choose to exit the industry at a cost (a loss of 1), with the incumbent receiving a payoff of 8. Alternatively, the entrant can stay, resulting in mutual losses (-5 each). Consequently, the entrant’s dominant response when faced with fighting is to withdraw since -1 is preferable to -5. This credible threat of withdrawal influences the incumbent’s decision-making process.
The incumbent, aware of this strategic response, anticipates the entrant’s withdrawal and thus prefers to avoid costly fights. Fighting would only occur if the incumbent perceives that the payoff from fighting (8) exceeds the payoff from accommodating or avoiding confrontation altogether. The critical insight here is that the presence of an exit option deters the incumbent from initiating conflict, leading to a more peaceful resolution where entry occurs without escalation.
This outcome underscores the importance of withdrawal rights as a strategic commitment device. They serve as a credible threat that influences incumbent behavior, ultimately benefiting the entrant. Without the option to withdraw, the entrant might face a costly fight or be deterred from entering altogether. Thus, the strategic environment with withdrawal options enables more efficient market entry and reduces unnecessary conflict, aligning incentives toward mutually beneficial outcomes.
Empirical evidence from industries such as telecommunications and airlines demonstrates that firms with exit strategies or contractual withdrawal provisions tend to face less aggressive competitive responses. These strategic mechanisms provide flexibility and bargaining power, thus fostering stability in market structures. The theoretical implications reinforce the importance of considering exit options in game-theoretic models, as they significantly affect equilibrium outcomes and industry dynamics.
In conclusion, the inclusion of a withdrawal option fundamentally alters the strategic landscape of entry games. It creates a credible deterrent against fighting, incentivizes peaceful coexistence, and enhances welfare for new entrants. The equilibrium, characterized by entry followed by withdrawal if attacked, demonstrates that the entrant is indeed better off with the ability to withdraw. This insight has profound implications for policymakers and firms designing strategic entry and competition policies, emphasizing the value of strategic flexibility in competitive markets.
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