Game Theory Talk 3- Introduction to Mechanism design

Summary:

1. Mechanism design is a field that deals with achieving desired outcomes by designing games with specific rules.
2. The concept of mechanism design is contrasted with game theory; the former designs games to obtain an outcome, while the latter analyzes given games to find outcomes.
3. A cake-cutting example illustrates mechanism design, where rules are set such that a cake is divided equitably between two children.
4. The 0-1 knapsack problem demonstrates an issue with hidden values known by owners only, leading to the preference elicitation problem.
5. The goal is to construct a game that elicits truthful reporting of these hidden values by aligning incentives appropriately.
6. A mathematical model of mechanism design involves social choice functions and utility functions, aiming to reward agents based on outcomes matching their true values.
7. An example of supplier selection problem illustrates the creation of social choice functions to ensure suppliers report true values for products.
8. A bad social choice function can lead suppliers to lie for better rewards, while a good one aligns their rewards with truthful reporting.
9. The talk concludes with a discussion on auction design in IPL, explaining how different strategies would elicit truthful bids and maximize expected value.

Key Questions and Answers:

How does mechanism design differ from game theory?
- Mechanism design is focused on creating a game with specific rules to ensure a particular outcome is achieved, while game theory is about analyzing existing games to predict outcomes.

How does the cake-cutting example explain mechanism design?
- The cake-cutting example shows how a game with specific rules (one child cuts the cake, and the other chooses a piece) can lead to an outcome where both children believe they have received a fair share, showcasing mechanism design in action.

What is the preference elicitation problem in mechanism design?
- The preference elicitation problem occurs when values are hidden, and agents may misreport their true values. In mechanism design, games must be created so that agents are incentivized to report their true values.

How is the concept of utility functions applied in mechanism design?
- Utility functions in mechanism design are used to assign rewards to players based on the outcomes and their true values, driving players to reveal their true preferences for maximum reward.

Why might a supplier lie about the value of their product in the mechanism design model?
- A supplier might lie if the designed game (social choice function) rewards them more for lying than telling the truth. This is an example of a poorly designed mechanism.

What is an implementable social choice function?
- An implementable social choice function is designed such that the best strategy for all players is to truthfully report their values, ensuring the mechanism elicits honest information.

Why might the auction strategy used in IPL not elicit truthful bidding?
- The current IPL auction strategy might not elicit truthful bidding because teams will bid higher than their actual valuation to ensure they win the player, which does not reflect their true valuation of the player.

Here are a few memorable quotes:
- "You want an outcome and for that you sort of make some rules."
- "Your entire mechanism design will be revolving around making the players say the truth."
- "Based on the reported values which you got, you determine an outcome."
- "The rough idea would be to give those outcomes where the player will be sort of forced to tell the truth."

Core Takeaway:
The core problem described is designing mechanisms that elicit truthful information from agents with hidden values. Not solving this can lead to suboptimal distribution of resources and rewards. To address this problem:
1. Create mechanisms that align players' incentives with truthful reporting, such as the cake-cutting strategy where one child cuts and the other chooses.
2. Utilize social choice functions to dictate outcomes in a way that maximizes agents' utility when they report truthfully.
3. Modify traditional auction designs to one where bidders are incentivized to bid their true valuation, like proposing a system where the highest bidder pays half their bid.

Tags here:
mechanism design, game theory, preference elicitation problem, social choice function, utility function, supplier selection problem, auctions