Integrating time step of optimization problem

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RWTH_FCN
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Re: Integrating time step of optimization problem

Post by RWTH_FCN » Fri Dec 06, 2019 4:40 pm

tomfid wrote:
Wed Aug 21, 2019 10:02 pm
I've attached two models, neither of which is really right, but both in the ballpark.

DEMAND AT PRICE elec 2.mdlDEMAND AT PRICE elec 1.mdl

#1 implements what I originally suggested, which is that everyone bids close to MAX( marg cost, expected price ). That actually implements collusion, and the price gets bid up to a high level. The missing piece is that it doesn't account for utilization. As long as the bidders are small relative to the market, they're price takers, and therefore they make money by pushing utilization as high as possible at the clearing price.

#2 implements that idea heuristically, but i didn't spend much time on it, and there's some discrete instability due to the 1hr time step. I'm sure it can be improved, but it expresses the basic idea.

I think the bottom line is that as long as the market is competitive and suppliers do a decent job of forming expectations, the market outcome will be pretty close to what the alloc functions yield without this behavioral detail.
Price development of model #2 is increasing which is contradictory to behavior of bidders in auction theory. I was wondering how can this assumption be implemented in the system dynamics perspective.

tomfid
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Re: Integrating time step of optimization problem

Post by tomfid » Fri Dec 06, 2019 4:58 pm

Not sure where the original thread is, but I think the problem may be that inclusion of expected price in bid formation is not rational or competitive, hence the apparent violation of theory.

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Re: Integrating time step of optimization problem

Post by RWTH_FCN » Fri Dec 06, 2019 6:06 pm

tomfid wrote:
Fri Dec 06, 2019 4:58 pm
Not sure where the original thread is, but I think the problem may be that inclusion of expected price in bid formation is not rational or competitive, hence the apparent violation of theory.
Yes, its related to the expected price. Actually, there is a trade-off for bidders which they trade-off between increasing the probability of winning the early auction and being better informed and increased expected payoff in later auction, so this trade-off leads bidders to bid lower. In the ther words, inclusion of learning from past events leads to bidding lower in further auctions.

tomfid
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Re: Integrating time step of optimization problem

Post by tomfid » Fri Dec 06, 2019 8:53 pm

Is there a reason to to have bidders bid at their own marginal cost, per theory?

RWTH_FCN
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Re: Integrating time step of optimization problem

Post by RWTH_FCN » Fri Dec 06, 2019 11:56 pm

tomfid wrote:
Fri Dec 06, 2019 8:53 pm
Is there a reason to to have bidders bid at their own marginal cost, per theory?
Its not competently marginal pricing because in discriminatory auction like pay as bid (PAB) auction bidders bid at least their cost ( it could be marginal cost or LCOE) plus a mark-up. Actually, the higher the bid, the lower probability for winning.

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Re: Integrating time step of optimization problem

Post by tomfid » Sat Dec 07, 2019 12:32 am

Ah - that explains the difference. Seems like a weird way to run a market, but if those are the rules, those are the rules.

Here's an idea:

Suppose generators bid at cost + markup

Make the markup a stock, which bidders adjust according to some pressures - e.g., maintaining a desired utilization (subject to price > cost), and relationship between bid and expected market clearing price.

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Re: Integrating time step of optimization problem

Post by RWTH_FCN » Sat Dec 07, 2019 5:36 pm

tomfid wrote:
Sat Dec 07, 2019 12:32 am
Ah - that explains the difference. Seems like a weird way to run a market, but if those are the rules, those are the rules.

Here's an idea:

Suppose generators bid at cost + markup

Make the markup a stock, which bidders adjust according to some pressures - e.g., maintaining a desired utilization (subject to price > cost), and relationship between bid and expected market clearing price.
Actually, it is not very weird in sequential acutions. This study (https://www.jstor.org/stable/1061354?se ... b_contents) demonstrates how sequential auctions have decreasing price development. Many other auctions such renewable auctions in the world also confirm this pattern.

Utilizization is a good point. But since bids of bidders in any auction are related to information transmission and learning from market, I tried to implement this concept in the model, so I multiplied it with pi-product of previous utilization:

Targeted price = MIN( price ceiling, marginal cost[supplier] + Utilization[supplier]*(1-Utilization of past[supplier])*MAX(0,Expected Price[supplier]-marginal cost[supplier]) )

If Utilization of past[supplier] = DELAY FIXED(Utilization[supplier], 1,Utilization[supplier]) does Utilization[supplier]*(1-Utilization of past[supplier]) represent Probibility( successful bid in round i)*PROD(unsuccessful bid in last rounds) ?

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