Some Applications of Strategic Games to...

Some Applications of Strategic Games to Procurement and Markets

Nicola Dimitri University of Siena (Italy) Rome March-April 2014

Some Applications of Strategic Games to

Procurement and Markets

Procurement Competitive Tendering 1/2

• Auctions One of the areas where Game Theory has been successfully applied is auction, competitive tendering, design.

• Starting from the early 80s (auctions for Oil Drills rights), going through the early 90s (world wide auctions for Spectrum privatization), game theory experts have been consulted both to design auctions as well as to providing suggestions on bidding strategies to competing participants.



Procurement Competitive Tendering 2/2

• The reason for game theory experts to be consulted was that bidding behavior, in auctions, is inherently strategic.

• Indeed suppliers participating to a competitive tendering typically face a fundamental trade-off between winning the competition and receiving a high compensation from the purchaser.

• For example, in a reversed lowest (best) - price procurement auction while a supplier submitting a very low price increases her likelihood of winning the competition, in case of victory she decreases her own financial benefits with respect to winning at a higher price.

• Therefore, for a supplier, winning a lowest price procurement competition does not depend only upon the price that she submits but also upon the price that her competitors submit.



Secret Offer Tendering 1/3 • The competitive tendering designs typically used in procurement are, or combine, two main

types of bidding mechanisms: competitions with secret offer (also called sealed-bid) and procurement auctions (also called dynamic auctions)

• These two formats could be applied to both lowest price, second lowest price, and Most Economic Advantageous Tender (MEAT) competitions.

• Secret Offer Tendering Competition In these kind of competition suppliers bid for a contract,

submitting offers without observing the other participants’ bid.

• In sales auctions they are called sealed-bid auctions. Some of the main advantages explaining why this format is so wide spread also in procurement are the following:

i) it can discourage, or mitigate, collusion among suppliers. ii) it can foster participation by a higher number of smaller firms. iii) it is relatively simple to organize for the buyer, and easy to understand and

manage for the suppliers.



Secret Offer Tendering 2/3 • Outbidding Though there could be multi-rounds competitive tendering with secret offers, in a

single round suppliers could not outbid each other. • Multi-rounds When the number of (one or more) rounds, or stages, is fixed and announced in

advance then if the last round is reached by more than one competitor, the final outcome could be more uncertain than when no upper limit to the number of rounds is predefined.

• Uncertainty Such uncertainty characterizing secret offer is a main element fostering participation.

Indeed if a weaker bidder, small firm for example, could reach the last round he could think of having the chance of beating a stronger one, and this would encourage participation.



Secret Offer Tendering 3/3 • Single Lot The secret offer mechanism allows the buyer to tender one or multiple lots. A

single lot competition stimulates firms to express economies of scale but, just because of the size of the supply contract, small firms may be prevented from participating to the tendering.

• Multiple lots With multiple lots the secret offer mechanism normally concerns each lot

separately. However, it is also possible to have secret offer tendering with package, combinatorial, offers. In such competitions firms are allowed to bid for both single lots as well as submitting offers conditional on being assigned groups of lots. Package bidding is a flexible design allowing small firms to bid on one lot, or few of them, as well as bigger ones to submit offers on groups of lots and express their economies of scale.



Dynamic Auctions 1/2

• Dynamic Auctions In dynamic auctions suppliers can outbid each other; namely they could observe what the rivals have offered and submit a better proposal.

• Though perhaps un-frequent in public procurement (possible

exception “Buying Solutions” OGC), they can enhance more favorable outcomes for the buyer when bidders are commonly uncertain on the value of the supply contract.



Dynamic Auctions 2/2 • Indeed, in a standard one round secret offer tendering, uncertainty on the value

of the supply contract may induce cautious bidding behavior, possibly generating non attractive outcomes for the buyer.

• Learning If suppliers truly compete then dynamic auctions can better diffuse, through their offers, their private information and induce more aggressive bidding behavior by participants.

• Explicit collusion However, when offers are publicly observable collusion can be better enforced since deviation, from the cartel agreement, could be observed and punished immediately within the same auction.

• Tacit Collusion Moreover, when multiple lots are auctioned simultaneously price offers could be used by firms to signal preferred lots, and to tacitly agree on softening overall competition.



Competitive Tendering and Game Theory 1/12

• Can GT help us making predictions in procurement competitive tendering ?

• Yes, by making use of the notion of NE.




• Example (Secret Offer Lowest Price Tendering) • Suppose two suppliers, A and B, competing for a supply contract.

• Reserve price, highest acceptable price for the supply contract, is R

• Suppliers cost for the contract is c(A)>c(B), with R >c(A)>c(B). B is more efficient than A.

• c(A) and c(B) represent the minimum price firms are willing to accept to execute the

contract.

• To avoid monetary losses, for the contract suppliers bid prices no lower than their costs, namely P(A) ≥ c(A) and P(B) ≥ c(B)

• If P(A)<P(B) then A gets the contract otherwise B obtains the contract.




• The buyer knows that B is more efficient than A, but does not know their values. Hence, organizes a competition to induce their disclosure.

• Firms instead know each other costs.

• Since B is more efficient, in case the two firms will submit the same price offer the object will go to B.

• If A gets the contract then his payoff will be P(A)-c(A), while if B gets it she obtains P(B)-c(B).

If they do not win the contract then they get 0. Namely, payoffs are given by the savings bidders can obtain by winning the contract, and receiving more than the minimum price they were willing to accept.

• Considering P(A) and P(B) as the strategies that, A and B, have to choose, what is a NE of the game?

• NE analysis provides some good news, but also some slightly bad ones




• The bad news is that, even with two firms, there will be an infinity of NE, so the prediction on firms’ offer can not be sharp.

• The good news is that at all NE B, the more efficient firm, will win the contract.

• Indeed, at all Nash Equilibria the two price offers are • [c(B)≤P(A)=P(B) ≤ c(A)]. • Indeed, if B expects A to offer c(B)≤P(A)≤c(A), then any price c(B)≤P(B)≤P(A) would allow B to

win.

• Among such winning prices, B would be best, maximize his payoff, offering the highest one, namely P(B)=P(A).

• Analogously, if A expects B to offer c(B)≤P(B)≤c(A), due to the tie-break rule has nothing best to do than losing the competition and get 0 payoff, rather than a negative payoff, which he would get in case of victory. One of the infinite ways to lose the competition is to offer P(A)=P(B).




• Why wouldn’t a pair of price such as [P(A)>c(A); P(B)=P(A)], where A still loses the auction by offering a price higher than c(A), be a NE?

• Because against P(A)>c(A) offering P(B)=P(A) is best reply for firm B.

• Indeed, B’s optimal reaction would be to offer the highest price that would allow B to win, namely P(B)=P(A).

• But if B does so then A could win the contract by offering a price P(A), slightly below P(B), but higher than c(A).

• Namely, if P(B)>c(A) then A can always “undercut” B; but B in turn would

“undercut” P(A) until they reach [P(A)=c(A); P(B)=c(A)],




• Two observations: • 1) The NE predicts an efficient outcome, namely the contract

goes to the most efficient firm B, the one with lower costs. • 2) The winner, firm B, gets a price P(B) which is typically

higher than c(B), namely than the lowest price B was willing to offer. So, in general, B obtains a strictly positive payoff in this case.




• Example (Second-Lowest Price Competitive Tendering; “Vickrey Auction”)

• Same two firms, A and B, of the previous example.

• Now the firm proposing the lowest price will win the procurement contract, however receiving the second lowest price from the buyer




• Proposed for sales auctions by the Nobel Laureate William Vickrey (1961);

however a similar mechanism was first used by Johan Wolfgang Goethe in 1797!

• Basically unknown in procurement as well as in other contexts (except to stamp collectors), until the advent of Internet Auctions. Indeed, e-Bay Auctions and Amazon Auctions are forms of Vickery auctions.

• This competitive tendering has one important characteristic; if firms submit as prices P(A)=c(A) and P(B)=c(B), namely their own costs, then independently of what the competitor bids they could not get a higher payoff by proposing a different price.

• Namely, submitting one’s contract cost is a weakly dominating strategy, and also a NE!




• The existence of such dominating strategy can greatly simplify firms decision making. Moreover, if firms follow that strategy the buyer will know exactly how much firms evaluate the contract, and learn useful information about their cost structure.

• In the previous, lowest price competitive tendering, such a dominating strategy does not exist.




• However, unlike the lowest-price tendering, there are NE where firm A, the one with the higher evaluation of the supply contract, could (inefficiently) win the competition.

• For example, the pair of prices [P(A)<c(B); P(B)>c(A)] is a NE. It is based on firm’s B expectation that A would propose an extremely low price, so that B would find it unprofitable to win the competition. B has a variety of ways to lose the competition, among which he could offer prices higher than c(A). From a social point of view, NE where A wins are inefficient, since the contract would go to the firm with higher costs for executing it.



Cournot Duopoly 1/5



Cournot Duopoly




• MEAT Tendering Supply contracts could be awarded according to the criterion of the Most Economic Advantageous Offer,

namely to the firm obtaining the highest price-quality score. In these types of competitions the buyer typically assigns the contract to the firm obtaining the highest score, typically calculated by a formula of the kind

S(q,p) = aS(q) – bS(p),

where S(q) and S(p) are the scores, respectively, associated to the qualitative and price component of the offer and a,b>0.

• The game theoretic analysis of multidimensional tendering can be developed along similar lines to the one followed for sales, ascending, auctions. Notice however that generalizing the Vickrey auction, to second scoring competitive tendering, allows more flexibility with respect to price-only. In such a competition the bidder offering the highest score wins and has to deliver a price-quality combination providing the second highest score submitted in the tender. This does not have to coincide necessarily with the price-quality combination proposed by the best rival in the competition.




• MEAT Tendering (Example) Suppose S(q,p) = q – p,

where S(q)=q and S(p)=p are the scores for quality and price, and a=b=1. Moreover, suppose

there two firms A and B. To produce “a level of quality equal to q” have cost functions given, respectively, by CA(q)=(q2)/2 and CB(q)= q.

• Then, under the condition that p ≥ C (q) it is clear that firm A could win the competition since by proposing quality q*=1 and a price p*= ½,= CA(1) he could obtain a maximum score equal to

SA(q=1,p=1/2) = 1 – ½ = ½ while the maximum score obtainable by B is SA(q,p) = q - CB(q)= q – q = 0 for all possible q.

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