1
$\begingroup$

Why is Dominant-Strategy Incentive Compatibility treated as such a ubiquitous virtue? In this lecture, the answer given from the perspective of a non-principal player is, "it's easy to play; you have an obvious strategy."

For most games that would be referred to as games in the colloquially sense, I would argue that strategic richness, the opposite of being strategyproof, is what imbues a game with enduring entertainment value over a long period of time. Strategyproofing in these games tends to be desirable when some extrinsic consideration, such as satisfying paying spectators, overrides the interests of the players, or when short term interests of players are prioritized over their long term interests. Even in other types of games such as auctions or road selection while driving, it seems plausible that strategic richness may be seen as a virtue, perhaps depending on the individual player's tastes and personality.

I do see how this simplicity could be directly beneficial to the principal. Whether it is ultimately beneficial to the principal may depend on how much the principal cares about the interests of the other players, i.e., through market incentives, whether the principal is able to convince the other players that their interests align with the principal's interests, i.e., by manufacturing or encouraging a negative sentiment toward design decision which produce strategic richness, whether the principal can hide strategic simplicity behind the appearance of strategic richness, etc. The point is that strategyproofing could be positive or negative depending on the game, but it is championed in mechanism design seemingly beyond what is warranted.

I am new to studying the subject, so perhaps I have a very blinkered view of the field. Are there tools available for maximizing strategic richness in contrast to those for strategyproofing? If not, is it because there is some theorem that strategically rich games are necessarily less efficient, i.e., do they all suffer from Braess's Paradox?

$\endgroup$
2
  • 1
    $\begingroup$ While I do not appreciate the ranting and raving nature of the question, this might be of interest: journals.uchicago.edu/doi/abs/10.1086/677350 $\endgroup$ Dec 9, 2022 at 1:48
  • $\begingroup$ @MichaelGreinecker I have taken out the rant and improved the tone of the question. As for the article, I think it only addresses the effect of information on players, not the effect of the structure of strategies on players. $\endgroup$
    – user10478
    Dec 11, 2022 at 2:56

2 Answers 2

2
$\begingroup$

The answer by VARulle is perfectly fine. I just want to add something and may repeat his point for completeness.

A mechanism designer often has a policy goal such as efficiently allocating a good to one of several buyers or implementing an envy-free/stable match between schools and students. Here, the designer just wants to reach this goal and is not interested in how much the players enjoy playing under the designed rules. In these examples, I find it reasonable to assume that students simply want to be assigned to the best possible school, and that the buyers just want to get the good for a low price. I don't believe such participants care a lot about the entertainment value of the game.

In the context of school choice, there is evidence that participants in non-strategyproof mechanisms are not very good at strategizing. In the context of first-price auctions, there is evidence that participants have a hard time bidding optimally. This makes sense because you need accurate beliefs about how others play and about their private information. This may be too much to ask for real people. In this sense, strategyproof mechanisms are seen as "leveling the playing field" because there is no advantage given to agents that are better informed or strategically more sophisticated. Such an advantage may be a design feature in a game in the colloquial sense, but it would be seen as unfair/undesirable in the context of my examples. In addition, the designer wants to maximize her objective function and if participants don't manage to play optimally due to the complexity, the desirable allocation is not implemented.

If the agents cared about how entertaining a game is, I don't think we have a way to formalize such a notion yet. We also do not have great formal notions on how easy a game is. I don't think a game with a dominant strategy is necessarily trivial. There are chess puzzles in which a single strategy yields a checkmate no matter what the other person plays, but for some puzzles even grandmasters do not see the solution immediately. Hence, just because a strategy exists that is best no matter what the others do it doesn't mean that everyone can find it easily or that finding it cannot be fun. In fact, there is a huge experimental literature showing that far from everyone plays optimally in strategyproof mechanisms. In this sense, economists are not converging towards your idea to make games more complex, but are looking for ways to make them even easier, see for instance, the notion of an obviously dominant strategy Li (2017).

$\endgroup$
3
  • 1
    $\begingroup$ My only qualm is the phrase "would be seen as unfair/undesirable in the context of my examples." I think looking for a "level playing field" only when outcomes are stratified by information/strategy is an equally good or better notion of fairness. For example, it would generally be seen as fair for a more informed/strategic trader to do better in financial markets, precisely because they've cultivated those abilities. As for desirability, if a game is repeated indefinitely, then players with a growth mentality (lower time preference) should find strategically rich auctions more desirable, $\endgroup$
    – user10478
    May 16, 2023 at 21:43
  • $\begingroup$ as they will be able to grow and improve their strategic performance over time. $\endgroup$
    – user10478
    May 16, 2023 at 21:44
  • 1
    $\begingroup$ I agree that it depends on the context which notion of fairness applies best. I think the notion of a strategyproof mechanisms as a "level playing field" comes form the school choice literature. See e.g. Pathak & Sönmez (2008) aeaweb.org/articles?id=10.1257/aer.98.4.1636 Here, I do find it unfair if kids of less sophisticated (for whatever reason) parents were disadvantaged. $\endgroup$
    – Bayesian
    May 17, 2023 at 11:13
3
$\begingroup$

The games played in mechanisms are not "games in the colloquial sense". Whatever players really value is represented by their payoffs, so if they value strategic richness of a game, this is already incorporated in their payoff functions. (Though it presumably wouldn't matter for how they play a given game.)

In a strategic interaction problem (a game in the technical sense), maximizing one's payoff usually requires formation of a belief about others' strategy choices, which can be quite demanding, e.g. if the game is a one-shot game. In such an environment the standard assumption that players will play a Bayes-Nash equilibrium might be implausible.

If a player has a dominant strategy, however, no such belief formation is required, which makes the game "easy to play". A mechanism designer who values robustness of outcomes would therefore prefer to find a DSIC mechanism.

$\endgroup$
2
  • 1
    $\begingroup$ I take it that games in the colloquial sense are pretty much a subset of games in the technical sense, maybe with a few outlier exceptions, so that, i.e., the designing of a game like chess could be studied by mechanism design? Surely it would be bad to design chess to have a dominant strategy. Even in something like an auction designed partially with entertainment in mind (perhaps an attraction in a vacation locale), it doesn't seem unreasonable that a format without a dominant strategy might be better at intellectually engaging people and improving their overall experience. I can't quite $\endgroup$
    – user10478
    Dec 11, 2022 at 3:12
  • $\begingroup$ see how incorporating these preferences into the payoffs obviates the possible benefit of considering non-DSIC mechanisms. $\endgroup$
    – user10478
    Dec 11, 2022 at 3:15

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.