What are some common game theory models used to analyze market competition and entry?

To understand this concept, consider OPEC. OPEC comprises oil-producing nations that operate in a Cournot Model. They control the supply of oil, and by adjusting their oil production, they influence global oil prices. However, the Cournot Model presents an interesting dilemma. On one hand, it suggests that these firms should collaborate and set output levels together to maximize their collective profit. This is because, in a Cournot oligopoly, the rational choice might appear to be collusion, where firms work together to control prices. But in real life, Game Theory shows that collusion is often unstable. Firms in Cournot Model may undercut each other to gain a larger share of the market, leading to price wars and less profit for everyone.

this might describe banking sector in Belgium where interest rates offered on savings accounts are not very responsive to increase in refinancing interest rates with ECB

One of the real-life examples of Bertrand's is the scenario of the gasoline market. In this setting, individual gas stations engage in a strategic pricing competition. Each gas station autonomously determines the price per gallon for its gasoline. Given that gasoline is a relatively homogeneous commodity, consumers, primarily motorists, select the gas station with the lowest posted price. This dynamic mirrors a competitive game where the aim is to attract customers by offering the most competitive pricing. However, factors such as proximity and additional amenities can influence consumer choices, introducing nuances into this pricing competition.

The Bertrand model of game theory is exemplified by the competition between two airlines offering identical services, such as Airline A and Airline B on the same route. They simultaneously set ticket prices and understand that consumers choose the lower-priced option. In this scenario, a fierce price war ensues, with both airlines continually reducing fares to attract passengers. This often leads to price convergence, where both airlines offer nearly identical low prices, erasing price as a differentiator. While consumers benefit from lower ticket prices, it reduces profit margins for the airlines, potentially to unsustainable levels. To maintain profitability, companies must find alternative means to differentiate themselves beyond price.

It is worth noting that: 1. The Stackelberg model is a specification of a Game of Incomplete Information. By definition, this implies other players (The Followers) will not always possess knowledge of the preferences (i.e. Payoff Function) of at least one player (The Leader) at every instantiation of a Strategy Profile. 2. The Stackelberg model is a modification and extension of Signaling Games that provides accommodation for multiple players (greater than 2) without necessarily being a Cooperative Game. By definition, this implies one player (The Leader) takes an action (The Signal) to convey information to other players (The Followers) before they can respond, where sending The Signal is mutually costly if it conveys false information.

Here are some additional insights and considerations about the model: - Symmetry: The Nash bargaining model assumes equal bargaining abilities among players. However, if one player has a distinct advantage, such as better alternatives, the outcome may tilt in their favor. - Threat Points: Often called "threat points," reservation values are the least a player will accept. If talks fail, players revert to these values. The difference between an agreement and this value shows the player's bargaining benefit. - Pareto Efficiency: The Nash solution ensures no deal can better one player without harming another.

In the airline industry, dominant players like Delta and American Airlines use their established infrastructure and customer base to deter new entrants, employing tactics like predatory pricing and enhancing loyalty programs. Potential newcomers, aware of these strategies, assess the market conditions and incumbents' actions before deciding on their market entry strategy, which might involve targeting underserved niches or presenting unique selling propositions. This play between incumbents and potential entrants, where each responds to the other's anticipated moves, embodies a representation of the entry deterrence model in game theory, often leading to a state of equilibrium where both can coexist by targeting different customers.

LLM companies use the deterrence model of Game Theory to ensure uninterrupted development of their tools & prevent any rogue player from disrupting their progress. It creates a threat of retaliation that is severe enough to deter any potential misbehavior. LLM companies invest heavily in R&D, IP, & legal to deter any potential rogue player from stealing or copying their technology. The deterrence model is effective because it creates a high barrier to entry for any potential rogue player. The cost of developing a competing technology from scratch or facing legal action for stealing IP is too high for most rogue players. By creating a strong deterrent, LLMs focus on their development without worrying about interruptions or disruptions.

Additional items to consider: Credible Threats: The incumbent's threats must be believable to deter entry effectively. Limit Pricing: Incumbents set prices just low enough to ward off entrants but maximize profit. Reputation: Incumbents with a history of aggressive responses can deter new entrants without explicit threats. Sunk Costs: These double-edged swords can deter entry but also lock incumbents into unprofitable competition. Strategic Barriers: Firms can use exclusive contracts, advertising, or proprietary tech to raise entry costs.