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Applied Category Theory for the Working Entrepreneur and Economist.

Since I suggested it, I thought I'd create a discussion group.

Discuss topics such as how to apply category theory to value theory, property theory, trade, contracts, and all the other odds and ends of economics and entrepreneurship.

Also, don't be afraid to hold and give a differing point of view. People of all economic backgrounds should feel welcome. Just don't get into huge arguments. In fact, I encourage you all to find a way to "translate" in a way differing economic points of views using the tools of category theory.

Comments

  • 1.

    Behavioural Economics

    In another thread (https://forum.azimuthproject.org/discussion/2058/introduction-marc-kaufmann), @MatthewDoty asked for "best papers in BE" and @MarcKauffman suggested the following:

    1. O'Donoghue and Rabin (1999), "Doing it now or later"
    2. Koszegi and Rabin (2009) "Reference-Dependent Consumption Plans"
    3. Loewenstein and Prelec (1998) "The Red and the Black"; totally not in the league as the other two in terms of being right, but it's really interesting
    4. Loewenstein, O'Donoghue, and Rabin (2003) "Projection Bias" (or some such); I overrate this, as it's what I (partially) work on
    5. DellaVigna (2009) "Psychology and Economics in the Field" (or something like that) is a great overview where the field was 10 years ago

    Marc also referred more generally to the works of Daniel Kahneman, Amos Tversky, George Loewenstein, Ted O'Donoghue, Matthew Rabin, Botond Koszegi, Paul Heidues, and Rani Spiegler.

    As a more recent and comprehensive overview I suggested Dhami's massive (1798 pages!) "The Foundations of Behavioral Economic Analysis" (Oxford University Press). I have only briefly skimmed this encyclopaedic reference and it seems quite good to me, though you should note that, unlike Marc, I am not an expert in BE. Marc also mentioned that an "Handbook in Behavioral Economics" is upcoming.

    Comment Source:# Behavioural Economics In another thread (https://forum.azimuthproject.org/discussion/2058/introduction-marc-kaufmann), @MatthewDoty asked for "best papers in BE" and @MarcKauffman suggested the following: 1. O'Donoghue and Rabin (1999), "Doing it now or later" 2. Koszegi and Rabin (2009) "Reference-Dependent Consumption Plans" 3. Loewenstein and Prelec (1998) "The Red and the Black"; totally not in the league as the other two in terms of being right, but it's really interesting 4. Loewenstein, O'Donoghue, and Rabin (2003) "Projection Bias" (or some such); I overrate this, as it's what I (partially) work on 5. DellaVigna (2009) "Psychology and Economics in the Field" (or something like that) is a great overview where the field was 10 years ago Marc also referred more generally to the works of Daniel Kahneman, Amos Tversky, George Loewenstein, Ted O'Donoghue, Matthew Rabin, Botond Koszegi, Paul Heidues, and Rani Spiegler. As a more recent and comprehensive overview I suggested Dhami's massive (1798 pages!) "The Foundations of Behavioral Economic Analysis" (Oxford University Press). I have only briefly skimmed this encyclopaedic reference and it seems quite good to me, though you should note that, unlike Marc, I am not an expert in BE. Marc also mentioned that an "Handbook in Behavioral Economics" is upcoming.
  • 2.

    Intuitions about this interface?A prioritary topic for apply categories? Your thoughts?Best

    Comment Source:Intuitions about this interface?A prioritary topic for apply categories? Your thoughts?Best
  • 3.

    I don't know enough about BE to tell if category theory can help organise the plethora of methods and behavioural theories in the field. But maybe it can help explore the consequences of individual-level behavioural assumptions at higher levels of aggregation (e.g., firms/markets/macro-economies).

    A major difficulty in going from single-agent to multi-agent settings is that "games" do not compose well in general: for example, the Nash equilibrium of two games played concurrently is not necessarily the natural composition of the Nash equilibria of the two individual games (e.g., you may have two markets where collusion among firms would not be an equilibrium if there were no connections between the markets, but collusion is sustainable when the same firms operate in both markets). Every time you change the environment (e.g., put the model of firm behaviour established for a given context into a larger context), all agents re-optimise for the new environment and you have to analyse everything from scratch.

    Perhaps, if we could model agents with simpler behavioural rules ("bounded rationality" of some sort), it would be easier to "move up one (aggregation) level" and category theory could help define what properties the behavioural rules would have to satisfy in order to allow easy aggregation.

    Or (non exclusive) CT could help define properties of the environment for which more complex behavioural rules (or even standard rationality) allow straightforward aggregation. I believe that @JulesHedges work on open games falls in this category (no pun intended).

    (btw, easy aggregation is obtained in standard general equilibrium theory - and, I believe, in the associated computable general equilibrium models used in climate science - mainly by assuming perfect competition whereby firms and consumers interact only via prices that they take as exogenously given)

    Comment Source:I don't know enough about BE to tell if category theory can help organise the plethora of methods and behavioural theories in the field. But maybe it can help explore the consequences of individual-level behavioural assumptions at higher levels of aggregation (e.g., firms/markets/macro-economies). A major difficulty in going from single-agent to multi-agent settings is that "games" do not compose well in general: for example, the Nash equilibrium of two games played concurrently is not necessarily the natural composition of the Nash equilibria of the two individual games (e.g., you may have two markets where collusion among firms would not be an equilibrium if there were no connections between the markets, but collusion is sustainable when the same firms operate in both markets). Every time you change the environment (e.g., put the model of firm behaviour established for a given context into a larger context), all agents re-optimise for the new environment and you have to analyse everything from scratch. Perhaps, if we could model agents with simpler behavioural rules ("bounded rationality" of some sort), it would be easier to "move up one (aggregation) level" and category theory could help define what properties the behavioural rules would have to satisfy in order to allow easy aggregation. Or (non exclusive) CT could help define properties of the environment for which more complex behavioural rules (or even standard rationality) allow straightforward aggregation. I believe that @JulesHedges work on open games falls in this category (no pun intended). (btw, easy aggregation is obtained in standard general equilibrium theory - and, I believe, in the associated computable general equilibrium models used in climate science - mainly by assuming perfect competition whereby firms and consumers interact only via prices that they take as exogenously given)
  • 4.
    edited May 17

    Interesting Valter Perhaps we could choose a single case /focus to study..i would suggest :the tragedy of commons..I think it could be framed as lack of cooperation.. http://science.sciencemag.org/content/162/385 Could one think the tendency of superexplotation of a public resource as an object and each person as a morphism from this object to it itself..this is a draft of a monoidal xxx? Best

    Comment Source:Interesting Valter Perhaps we could choose a single case /focus to study..i would suggest :the tragedy of commons..I think it could be framed as lack of cooperation.. http://science.sciencemag.org/content/162/385 Could one think the tendency of superexplotation of a public resource as an object and each person as a morphism from this object to it itself..this is a draft of a monoidal xxx? Best
  • 5.
    edited May 18

    Hi Pierre, The idea of starting with a "game" that is very well understood in the economics literature makes sense, but I suspect the Tragedy of the Commons may be too ambitious for the first target. Anyway, a couple of comments:

    1. I do not quite see how you would define "the tendency of superexplotation of a public resource".

    2. If you define morphisms as arrows from agents to some object (only one object? are you trying to get a group structure?), then it seems more natural to define the object as the state of the system. The issue is then getting a suitable definition of state for this problem. The naive one (e.g., the fish population distribution in the context of overfishing as the Tragedy) would be inadequate if we wanted to explore the issue of institutional design (i.e., the possible implicit or explicit contracts among agents) that is the really interesting one in the Tragedy of the Commons context.

    We could start with the simplest case in which there are no such contracts and the "tragedy" occurs, but even here we would be dealing with a dynamic game (e.g., you fish, I fish, then we want to fish again and there may or may not be any fish left) so I guess we'd need at least something like Petri Nets/reaction networks.

    (btw, there have been some attempts to use Petri Nets in economics - e.g, a quick web search came up with http://faculty.econ.ucdavis.edu/faculty/bonanno/PDF/petri and http://esc.vscc.ac.ru/article/568?_lang=en - but they did not get much traction.)

    I think I will wait a bit longer before jumping into modelling, but I definitely do not mean to discourage you (or any others) from giving this a go.

    P.S. The link to the Science article does not seem to work.

    P.P.S. I just found that the connection between game theory and Petri Nets had already been mentioned in the Azimuth forum! https://forum.azimuthproject.org/discussion/1071/game-theory-and-petri-nets

    Comment Source:Hi Pierre, The idea of starting with a "game" that is very well understood in the economics literature makes sense, but I suspect the Tragedy of the Commons may be too ambitious for the first target. Anyway, a couple of comments: 1. I do not quite see how you would define "the tendency of superexplotation of a public resource". 2. If you define morphisms as arrows from agents to some object (only one object? are you trying to get a group structure?), then it seems more natural to define the object as the state of the system. The issue is then getting a suitable definition of state for this problem. The naive one (e.g., the fish population distribution in the context of overfishing as the Tragedy) would be inadequate if we wanted to explore the issue of institutional design (i.e., the possible implicit or explicit contracts among agents) that is the really interesting one in the Tragedy of the Commons context. We could start with the simplest case in which there are no such contracts and the "tragedy" occurs, but even here we would be dealing with a dynamic game (e.g., you fish, I fish, then we want to fish again and there may or may not be any fish left) so I guess we'd need at least something like Petri Nets/reaction networks. (btw, there have been some attempts to use Petri Nets in economics - e.g, a quick web search came up with http://faculty.econ.ucdavis.edu/faculty/bonanno/PDF/petri and http://esc.vscc.ac.ru/article/568?_lang=en - but they did not get much traction.) I think I will wait a bit longer before jumping into modelling, but I definitely do not mean to discourage you (or any others) from giving this a go. P.S. The link to the Science article does not seem to work. P.P.S. I just found that the connection between game theory and Petri Nets had already been mentioned in the Azimuth forum! https://forum.azimuthproject.org/discussion/1071/game-theory-and-petri-nets
  • 6.
    edited May 18

    Hi Pierre and Valter, in 2002, I wrote a paper An Economy for Giving Everything Away in which I bring out both the compatibility and duality of an economy based on maximizing happiness (classical economics) and minimizing anxiety (an economy for giving everything away). In particular, minimizing anxiety means avoiding having too much money (and too many obligations) as well as too little money (which causes problems for others). I consider their implications, as strategies, in three modes:

    • In the little things in life, like getting ahead in traffic, a strategy of maximizing happiness will push to win in every case, will calculate every decision, whereas a strategy of minimizing anxiety will avoid such calculations and readily give way, "You go first".
    • In the middle things in life, like where to eat lunch, both strategies will let the market decide. Maximizing and minimizing have the same calculus and are compatible.
    • In the big things in life, like what to do with my life, what job to take, maximizing happiness will again obey the market as a selfish individual, whereas minimizing anxiety will consider, not what the market thinks, but what do I myself think is best use of my talents for all?

    Thus one can pursue a dissident strategy of minimizing anxiety and act "normally" in many matters of life. But the strategy will stick out in the little things in life but especially the big things in life.

    As regards modeling, what this suggests is that strategies (evaluations) are functors between environments, that is, between the Market of possibilities and the personal frameworks F1, F2,..., FN that individuals have. One strategy maps onto Happiness and maximizes that whereas another strategy maps onto Anxiety and minimizes that. This brings out the mental expectations - the mental environment - onto which we are mapping the market environment. So objects are Environments, and strategies/evaluations are functors between Environments, but notably, from the Market environment M to various evaluatory Frameworks F1,F2, ... FN.

    This might be relevant for analyzing the tragedy of the commons.

    Comment Source:Hi Pierre and Valter, in 2002, I wrote a paper [An Economy for Giving Everything Away](http://www.ms.lt/papers/2002-An-Economy-For-Giving-Everything-Away.pdf) in which I bring out both the compatibility and duality of an economy based on maximizing happiness (classical economics) and minimizing anxiety (an economy for giving everything away). In particular, minimizing anxiety means avoiding having too much money (and too many obligations) as well as too little money (which causes problems for others). I consider their implications, as strategies, in three modes: * In the little things in life, like getting ahead in traffic, a strategy of maximizing happiness will push to win in every case, will calculate every decision, whereas a strategy of minimizing anxiety will avoid such calculations and readily give way, "You go first". * In the middle things in life, like where to eat lunch, both strategies will let the market decide. Maximizing and minimizing have the same calculus and are compatible. * In the big things in life, like what to do with my life, what job to take, maximizing happiness will again obey the market as a selfish individual, whereas minimizing anxiety will consider, not what the market thinks, but what do I myself think is best use of my talents for all? Thus one can pursue a dissident strategy of minimizing anxiety and act "normally" in many matters of life. But the strategy will stick out in the little things in life but especially the big things in life. As regards modeling, what this suggests is that strategies (evaluations) are functors between environments, that is, between the Market of possibilities and the personal frameworks F1, F2,..., FN that individuals have. One strategy maps onto Happiness and maximizes that whereas another strategy maps onto Anxiety and minimizes that. This brings out the mental expectations - the mental environment - onto which we are mapping the market environment. So objects are Environments, and strategies/evaluations are functors between Environments, but notably, from the Market environment M to various evaluatory Frameworks F1,F2, ... FN. This might be relevant for analyzing the tragedy of the commons.
  • 7.

    Hi Valter...i did try to capture some possible invariant "pattern" as an object, despite the subject enrolled, in a monoidal categorie..but i feel one could detail it as you did devise ...

    Hi Andrius..interesting ideas..thanks for sharing..I will try to figure out how to use it.

    best

    Comment Source:Hi Valter...i did try to capture some possible invariant "pattern" as an object, despite the subject enrolled, in a monoidal categorie..but i feel one could detail it as you did devise ... Hi Andrius..interesting ideas..thanks for sharing..I will try to figure out how to use it. best
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