Advanced Microeconomics II: Game Theory and Information Economics

Advanced Microeconomics II represents a significant leap from the foundational theories of consumer choice and competitive markets. It delves into the complexities of strategic interaction and the implications of imperfect information. While introductory microeconomics often assumes that agents are price-takers operating in environments with perfect information, real-world markets function differently. This course analyzes how rational agents make decisions when their outcomes depend on the actions of others (Game Theory) and when they lack complete knowledge about relevant variables (Information Economics).

Part I: Game Theory

Game Theory is the study of mathematical models of strategic interaction among rational decision-makers. Unlike standard optimization problems where an agent maximizes utility given a fixed environment, in game theory, the environment includes other agents who are also maximizing their own utility.

Non-Cooperative Games and Nash Equilibrium

The cornerstone of non-cooperative game theory is the concept of Nash Equilibrium. Named after John Nash, a Nash Equilibrium is a set of strategies, one for each player, such that no player has an incentive to deviate from their chosen strategy after considering an opponent's choice. In other words, every player is choosing the best response to the strategies chosen by the others.

While pure-strategy Nash Equilibria exist in many games, some scenarios require randomized strategies known as Mixed Strategies, where players choose a probability distribution over possible actions. This is particularly relevant in zero-sum games, such as matching pennies or sports penalties, where predictability is a disadvantage.

Dynamic Games and Credibility

Static games assume players move simultaneously. However, many economic interactions occur sequentially. Dynamic Games analyze these situations, accounting for the order of moves and the ability of players to observe past actions before making their own decisions.

A critical refinement of Nash Equilibrium in dynamic settings is Subgame Perfect Equilibrium (SPE), often derived through Backward Induction. SPE eliminates non-credible threatspromises or threats that a player would not actually carry out if the time came to act. For example, a firm threatening to engage in a price war if a competitor enters the market is only credible if the cost of the price war is less than the cost of accommodation.

Repeated Games

When players interact repeatedly over time, the structure of the game changes fundamentally. In Infinitely Repeated Games, cooperation can often be sustained even when it is not rational in a one-shot interaction (such as in the Prisoner's Dilemma). Strategies like "Grim Trigger" or "Tit-for-Tat" allow players to punish defection in future periods, thereby incentivizing cooperative behavior in the present. This relies on the shadow of the futurethe present value of future cooperation outweighs the short-term gain from cheating.

Part II: Information Economics

Information Economics relaxes the assumption of perfect information. It studies how information asymmetrywhere one party has more or better information than the otheraffects economic outcomes. This field explains market failures that standard competitive models cannot explain and provides mechanisms to mitigate these inefficiencies.

Adverse Selection

Adverse Selection occurs when a lack of symmetric information before a transaction (hidden information) leads to market failure. A classic example is Akerlofs "Market for Lemons." In the used car market, sellers know the quality of their cars, but buyers do know. Because buyers are only willing to pay an average price, high-quality sellers ("peaches") exit the market, leaving only low-quality cars ("lemons"). This unraveling process can destroy the market entirely. Solutions include signaling (the informed party acts to reveal their type) and screening (the uninformed party creates a mechanism to elicit the truth).

Moral Hazard

Moral Hazard arises after a transaction takes place when one party changes their behavior to the detriment of another because they do not bear the full consequences of their actions (hidden action). This is prevalent in insurance markets and principal-agent relationships. For instance, an individual with full health insurance may overconsume medical care because they do not pay the marginal cost. Similarly, a manager (agent) may shirk if the owner (principal) cannot perfectly monitor their effort. Contracts must be designed to align incentives, often through "pay-for-performance" structures or deductibles and co-pays.

Principal-Agent Problems

The Principal-Agent framework formalizes the challenges of moral hazard. The principal designs a contract to induce the agent to act in the principal's best interest. However, the principal faces constraints: they must respect the agents Participation Constraint (the agent must be willing to accept the contract) and the Incentive Compatibility Constraint (the agent must prefer to perform the desired action rather than shirk). Optimal contract theory analyzes how to balance risk-sharing and incentives. If the agent is risk-averse and the principal is risk-neutral, the principal should insure the agent, but full insurance destroys incentives. Thus, the optimal contract usually involves sharing risks.

Part III: Game Theory with Incomplete Information

Advanced Microeconomics II combines strategic interaction with information asymmetry through Bayesian Games. In these games, players have incomplete information about the "payoff-relevant" characteristics of other players (such as their costs, valuation, or type).

The solution concept here is the Bayesian Nash Equilibrium. In this equilibrium, each player chooses a strategy that maximizes their expected utility, given their beliefs about the types of the other players. A subset of this is the Perfect Bayesian Equilibrium, which applies to dynamic games of incomplete information, requiring that beliefs be updated rationally according to Bayes' Rule whenever possible.

Signaling and Screening

To overcome adverse selection, informed agents may send signals. Education, for example, can serve as a signal of productivity in job markets (Spence signaling model). For a signal to be effective, it must be costly in a way that differs between typeshigh-productivity workers find obtaining education less costly than low-productivity workers. Conversely, screening occurs when the uninformed party offers a menu of contracts (e.g., different insurance plans with different deductibles) designed so that different types self-select into the appropriate contract.

Part IV: Mechanism Design

Mechanism Design, often called "reverse game theory," asks the following question: Given a desired social goal, what rules or mechanisms can be implemented to achieve that goal given that agents are private and self-interested? It is the engineering side of economics.

A central result in this field is the Revelation Principle. It states that if a social goal can be achieved by any mechanism, it can also be achieved by a direct mechanism where agents truthfully report their private information to a central authority. This simplifies the analysis significantly, allowing economists to focus on designing incentive-compatible truthful revelation mechanisms.

Auctions

Auctions are a prime application of mechanism design. Different auction formatsFirst-Price Sealed-Bid, Second-Price Sealed-Bid (Vickrey), English, and Dutchyield different outcomes. The Revenue Equivalence Theorem shows that under certain conditions (risk neutrality, independent private values, and standard auction formats), all auctions yield the same expected revenue to the seller. However, when these assumptions are violated (e.g., with common values or risk-averse bidders), the choice of auction format matters critically for efficiency and revenue.

Conclusion

Advanced Microeconomics II provides the analytical toolkit necessary to understand modern economic theory. From the strategic maneuvers in oligopolistic markets to the structural challenges of contracting under uncertainty, game theory and information economics offer profound insights into human behavior and market institutions. By modeling the world as it isstrategic, uncertain, and information-pooreconomists can better predict outcomes and design policies and markets that improve social welfare.